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[2] (./main.toc
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Chapter 1.
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[]\T1/ptm/m/n/10.95 Probabilistic gen-er-a-tion of fi-nite sim-ple groups, see 
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[6]
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[]\T1/ptm/m/n/10.95 A per-haps more suit-able overview of these changes is give
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[7]
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\T1/ptm/m/n/10.95 struc-tions has been added; where pos-si-ble, these con-struc
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[9]
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[]\T1/ptm/m/n/10.95 There is now a de-fault \T1/cmtt/m/n/10.95 InfoText \T1/ptm
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[]\T1/ptm/m/n/10.95 Several at-tribute val-ues for char-ac-ter ta-bles, such as
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\T1/ptm/m/n/10.95 First of all, of course sev-eral char-ac-ter ta-bles were add
ed; for an overview, see the file
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[12]
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\T1/ptm/m/n/10.95 and \T1/cmtt/m/n/10.95 gap4/test.gi\T1/ptm/m/n/10.95 . How-ev
er, cur-rently they are not doc-u-mented. The new file
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[13] [14]
Chapter 2.
[15

] [16] [17] [18] [19]
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[][]\T1/ptm/b/n/12 Example: Cer-tain el-e-men-tary abelian sub-groups in qua-si
sim-ple groups
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[29] [30] [31] [32] [33] [34] [35] [36] [37] [38]
Chapter 3.
[39

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[40]
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[]$\OML/ztmcm/m/it/10.95 .$\T1/cmtt/m/n/10.95 AllCharacterTableNames(\T1/cmtt/m
/sl/10.95 [func, val, ...[, OfThose, func]]: OrderedBy :=
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[]\T1/ptm/m/n/10.95 For the sake of ef-fi-ciency, the at-tributes whose names a
re listed in
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[]\T1/ptm/m/n/10.95 (Note that the al-phabti-cal or-der-ing could also be achie
ved by en-ter-ing \T1/cmtt/m/n/10.95 OrderedBy:=
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[]$\OML/ztmcm/m/it/10.95 .$\T1/cmtt/m/n/10.95 OneCharacterTableName(\T1/cmtt/m/
sl/10.95 [func, val, ...[, OfThose, func]]: OrderedBy := func\T1/cmtt/m/n/10.95
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\T1/ptm/m/n/10.95 re-turns the \T1/cmtt/m/n/10.95 Identifier \T1/ptm/m/n/10.95 
(\T1/ptm/b/n/10.95 Reference: Iden-ti-fier for char-ac-ter ta-bles\T1/ptm/m/n/1
0.95 ) value of a char-
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\T1/ptm/m/n/10.95 ac-ter ta-ble in the \T1/phv/m/n/10.95 GAP \T1/ptm/m/n/10.95 
Char-ac-ter Ta-ble Li-brary that is per-mu-ta-tion equiv-a-lent to
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[] \T1/ptm/m/n/10.95 (see \T1/cmtt/m/n/10.95 TransformingPermutationsCharacterT
ables \T1/ptm/m/n/10.95 (\T1/ptm/b/n/10.95 Reference: Trans-form-
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\T1/ptm/b/n/10.95 ing-Per-mu-ta-tion-sChar-ac-terTa-bles\T1/ptm/m/n/10.95 )) if
 such a char-ac-ter ta-ble ex-ists, and \T1/cmtt/m/n/10.95 fail \T1/ptm/m/n/10.
95 oth-er-wise.
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[]\T1/ptm/m/n/10.95 Let [] be an or-di-nary char-ac-ter ta-ble from the \T1/phv
/m/n/10.95 GAP \T1/ptm/m/n/10.95 Char-ac-ter Ta-ble Li-brary.
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[]\T1/ptm/m/n/10.95 For an or-di-nary char-ac-ter ta-ble [], this func-tion re-
turns \T1/cmtt/m/n/10.95 true \T1/ptm/m/n/10.95 if the list re-turned by
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[47]
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[]\T1/ptm/m/n/10.95 If [] has the form \T1/cmtt/m/n/10.95 [ $\OML/ztmcm/m/it/10
.95 funcname$\T1/cmtt/m/n/10.95 , $\OML/ztmcm/m/it/10.95 args$ \T1/cmtt/m/n/10.
95 ] \T1/ptm/m/n/10.95 and oc-curs in the list re-turned by
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\T1/cmtt/m/n/10.95 GroupInfoForCharacterTable \T1/ptm/m/n/10.95 ([][]3.3.1[][])
 when called with a char-ac-ter ta-ble $\OML/ztmcm/m/it/10.95 tbl$\T1/ptm/m/n/1
0.95 , say, then
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[]\T1/ptm/m/n/10.95 The string\T1/cmtt/m/n/10.95 "GroupForTom" \T1/ptm/m/n/10.9
5 may oc-cur in the en-tries of the list re-turned by
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[]\T1/ptm/m/n/10.95 The string\T1/cmtt/m/n/10.95 "AtlasStabilizer" \T1/ptm/m/n/
10.95 may oc-cur in the en-tries of the list re-turned by
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[]\T1/cmtt/m/n/10.95 DeligneLusztigNames \T1/ptm/m/n/10.95 called with a string
 [], calls it-self with the ar-gu-ment
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[]\T1/ptm/m/n/10.95 an overview of the ``atomic ir-ra-tional-i-ties'' that oc-c
ur in \T1/phv/m/n/10.95 At-las \T1/ptm/m/n/10.95 char-ac-ter ta-bles (see
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[]\T1/ptm/m/n/10.95 an overview of the lists of im-prove-ments to the \T1/phv/m
/n/10.95 At-las \T1/ptm/m/n/10.95 of Fi-nite Groups (see
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\T1/ptm/m/n/10.95 The func-tions \T1/cmtt/m/n/10.95 BrowseCTblLibInfo \T1/ptm/m
/n/10.95 ([][]3.5.2[][]), \T1/cmtt/m/n/10.95 BrowseCommonIrrationalities
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\T1/ptm/m/n/10.95 ([][]3.5.3[][]), \T1/cmtt/m/n/10.95 BrowseCTblLibDifferences 
\T1/ptm/m/n/10.95 ([][]3.5.4[][]), \T1/cmtt/m/n/10.95 BrowseAtlasContents \T1/p
tm/m/n/10.95 ([][]3.5.5[][]), and
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[]\T1/ptm/m/n/10.95 When ar-gu-ments [], [], [] are given that are ad-mis-si-bl
e ar-gu-ments for
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[52] [53] [54]
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[]\T1/ptm/m/n/10.95 The full func-tion-al-ity of the func-tion \T1/cmtt/m/n/10.
95 NCurses.BrowseGeneric \T1/ptm/m/n/10.95 (\T1/ptm/b/n/10.95 Browse:
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[55] [56]
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[]\T1/ptm/m/n/10.95 The string that is shown by \T1/cmtt/m/n/10.95 DisplayAtlas
Contents \T1/ptm/m/n/10.95 can be com-puted us-ing
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[57] [58]
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[]\T1/ptm/m/n/10.95 More gen-er-ally, [] can be an ad-mis-si-ble name for a cha
r-ac-ter with known
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[]\T1/ptm/m/n/10.95 The full func-tion-al-ity of the func-tion \T1/cmtt/m/n/10.
95 NCurses.BrowseGeneric \T1/ptm/m/n/10.95 (\T1/ptm/b/n/10.95 Browse:
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[]\T1/ptm/m/n/10.95 Currently \T1/cmtt/m/n/10.95 IdentifierOfMainTable \T1/ptm/
m/n/10.95 ([][]3.6.2[][]) does not re-turn \T1/cmtt/m/n/10.95 fail \T1/ptm/m/n/
10.95 for $\OML/ztmcm/m/it/10.95 t[]$ \T1/ptm/m/n/10.95 if
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\T1/cmtt/m/n/10.95 KnowsSomeGroupInfo \T1/ptm/m/n/10.95 ([][]3.3.2[][]), \T1/cm
tt/m/n/10.95 IsNontrivialDirectProduct \T1/ptm/m/n/10.95 ([][]3.3.7[][]), \T1/c
mtt/m/n/10.95 DeligneLusztigNames
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[]\T1/ptm/m/n/10.95 Without this method, it would be im-pos-si-ble to use \T1/c
mtt/m/n/10.95 InfoText \T1/ptm/m/n/10.95 in calls to
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[66]
Chapter 4.
[67

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\T1/ptm/m/n/10.95 ta-bles is stored us-ing the at-tributes \T1/cmtt/m/n/10.95 C
lassParameters \T1/ptm/m/n/10.95 (\T1/ptm/b/n/10.95 Reference: Class-Pa-ram-e-t
ers\T1/ptm/m/n/10.95 ) and
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[69] [70]
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[]\T1/ptm/m/n/10.95 For a record [] rep-re-sent-ing a generic char-ac-ter ta-bl
e, and a pa-ram-e-ter value [],
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[71] [72]
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[]\T1/ptm/m/n/10.95 In the spe-cial-ized ta-ble, the \T1/cmtt/m/n/10.95 ClassPa
rameters \T1/ptm/m/n/10.95 (\T1/ptm/b/n/10.95 Reference: Class-Pa-ram-e-ters\T1
/ptm/m/n/10.95 ) and
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[]\T1/ptm/m/n/10.95 Any \T1/phv/m/n/10.95 CAS \T1/ptm/m/n/10.95 ta-ble is ac-ce
s-si-ble by each of its \T1/phv/m/n/10.95 CAS \T1/ptm/m/n/10.95 names (ex-cept 
if stated oth-er-wise in
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[]\T1/ptm/m/n/10.95 Probably the eas-i-est change is to \T1/ptm/m/it/10.95 add 
new ad-mis-si-ble names \T1/ptm/m/n/10.95 to li-brary ta-bles, in or-
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\T1/ptm/m/n/10.95 checks the class fu-sions that are stored on the ta-ble $\OML
/ztmcm/m/it/10.95 tbl$\T1/ptm/m/n/10.95 : No du-pli-cates shall oc-cur,
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[94] [95]
Chapter 5.
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[]\T1/ptm/m/n/10.95 Let the ar-gu-ments be as de-scribed for \T1/cmtt/m/n/10.95
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[]\T1/ptm/m/n/10.95 Let the ar-gu-ments be as de-scribed for \T1/cmtt/m/n/10.95
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\T1/cmtt/m/n/10.95 PossibleActionsForTypeGS3 \T1/ptm/m/n/10.95 re-turns the set
 of those ta-ble au-to-mor-phisms
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\T1/ptm/m/n/10.95 (see \T1/cmtt/m/n/10.95 AutomorphismsOfTable \T1/ptm/m/n/10.9
5 (\T1/ptm/b/n/10.95 Reference: Au-to-mor-phism-sOfT-able\T1/ptm/m/n/10.95 )) o
f [] that can be
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[]$\OML/ztmcm/m/it/10.95 .$\T1/cmtt/m/n/10.95 PossibleCharacterTablesOfTypeGV4(
\T1/cmtt/m/sl/10.95 tblG, tblsG2, acts, identifier[,
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[]$\OML/ztmcm/m/it/10.95 .$\T1/cmtt/m/n/10.95 PossibleCharacterTablesOfTypeGV4(
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[]\T1/ptm/m/n/10.95 Let the ar-gu-ments be as de-scribed for \T1/cmtt/m/n/10.95
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[]$\OML/ztmcm/m/it/10.95 .$\T1/cmtt/m/n/10.95 CharacterTableOfIndexTwoSubdirect
Product(\T1/cmtt/m/sl/10.95 tblH1, tblG1, tblH2, tblG2,
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[]$\OML/ztmcm/m/it/10.95 .$\T1/cmtt/m/n/10.95 ConstructIndexTwoSubdirectProduct
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[]\T1/ptm/m/n/10.95 Called with one ar-gu-ment [], an or-di-nary char-ac-ter ta
-ble of the group $\OML/ztmcm/m/it/10.95 G$\T1/ptm/m/n/10.95 , say,
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\T1/cmtt/m/n/10.95 ConstructIndexTwoSubdirectProductInfo \T1/ptm/m/n/10.95 an-a
-lyzes the pos-si-bil-i-ties to con-struct
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[] \T1/ptm/m/n/10.95 from char-ac-ter ta-bles of sub-groups $\OML/ztmcm/m/it/10
.95 H[]$\T1/ptm/m/n/10.95 , $\OML/ztmcm/m/it/10.95 H[]$ \T1/ptm/m/n/10.95 and f
ac-tor groups $\OML/ztmcm/m/it/10.95 G[]$\T1/ptm/m/n/10.95 , $\OML/ztmcm/m/it/1
0.95 G[]$\T1/ptm/m/n/10.95 , us-ing
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[]\T1/ptm/m/n/10.95 Called with five ar-gu-ments, the or-di-nary char-ac-ter ta
-bles of $\OML/ztmcm/m/it/10.95 G$\T1/ptm/m/n/10.95 , $\OML/ztmcm/m/it/10.95 H[
]$\T1/ptm/m/n/10.95 , $\OML/ztmcm/m/it/10.95 G[]$\T1/ptm/m/n/10.95 , $\OML/ztmc
m/m/it/10.95 H[]$\T1/ptm/m/n/10.95 , $\OML/ztmcm/m/it/10.95 G[]$\T1/ptm/m/n/10.
95 ,
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\T1/cmtt/m/n/10.95 ConstructIndexTwoSubdirectProductInfo \T1/ptm/m/n/10.95 re-t
urns a list that can be used as the
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\T1/ptm/m/n/10.95 As for the con-struc-tion of Brauer char-ac-ter ta-bles from 
known ta-bles, the func-tions
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\T1/cmtt/m/n/10.95 PossibleCharacterTablesOfTypeMGA \T1/ptm/m/n/10.95 ([][]5.1.
1[][]), \T1/cmtt/m/n/10.95 CharacterTableOfTypeGS3 \T1/ptm/m/n/10.95 ([][]5.2.1
[][]), and
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[]\T1/ptm/m/n/10.95 Note that the ta-ble head of the $\OML/ztmcm/m/it/10.95 p$\
T1/ptm/m/n/10.95 -modular Brauer ta-ble of $\OML/ztmcm/m/it/10.95 H$\T1/ptm/m/n
/10.95 , in gen-eral with-out the
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