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Chapter 1.
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\OT1/pcr/m/n/10.95 http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc/ [][] \
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[]\OT1/ptm/m/n/10.95 download the pack-age archive \OT1/pcr/m/n/10.95 monoid3r1
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[10]
Chapter 2.

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Chapter 3.
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[]\OT1/ptm/m/n/10.95 the sec-ond en-try is a list of per-mu-ta-tions \OT1/pcr/m
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Chapter 4.
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[]\OT1/ptm/m/n/10.95 if \OT1/pcr/m/n/10.95 C \OT1/ptm/m/n/10.95 sat-is-fies \OT
1/pcr/m/n/10.95 IsGreensRClass \OT1/ptm/m/n/10.95 (\OT1/ptm/b/n/10.95 Reference
: Is-Green-sR-Class\OT1/ptm/m/n/10.95 ), then \OT1/pcr/m/n/10.95 GreensRClassDa
ta
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\OT1/ptm/m/n/10.95 re-turns an ob-ject in the cat-e-gory \OT1/pcr/m/n/10.95 IsG
reensRClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]) with rep-re-sen-ta-tion
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[28]
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\OT1/ptm/m/n/10.95 The com-po-nents \OT1/pcr/m/n/10.95 strongorb\OT1/ptm/m/n/10
.95 , \OT1/pcr/m/n/10.95 perms\OT1/ptm/m/n/10.95 , and \OT1/pcr/m/n/10.95 schut
z \OT1/ptm/m/n/10.95 are ob-tained us-ing the func-tion
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[]\OT1/ptm/m/n/10.95 if \OT1/pcr/m/n/10.95 C \OT1/ptm/m/n/10.95 sat-is-fies \OT
1/pcr/m/n/10.95 IsGreensLClass \OT1/ptm/m/n/10.95 (\OT1/ptm/b/n/10.95 Reference
: Is-GreensLClass\OT1/ptm/m/n/10.95 ), then \OT1/pcr/m/n/10.95 GreensLClassData

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\OT1/ptm/m/n/10.95 re-turns an ob-ject in the cat-e-gory \OT1/pcr/m/n/10.95 IsG
reensLClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]) with rep-re-sen-ta-tion
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[29]
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[]\OT1/ptm/m/n/10.95 if \OT1/pcr/m/n/10.95 C \OT1/ptm/m/n/10.95 sat-is-fies \OT
1/pcr/m/n/10.95 IsGreensHClass \OT1/ptm/m/n/10.95 (\OT1/ptm/b/n/10.95 Reference
: Is-Green-sH-Class\OT1/ptm/m/n/10.95 ), then \OT1/pcr/m/n/10.95 GreensLClassDa
ta
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\OT1/ptm/m/n/10.95 re-turns an ob-ject in the cat-e-gory \OT1/pcr/m/n/10.95 IsG
reensHClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]) with rep-re-sen-ta-tion
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[]\OT1/ptm/m/n/10.95 if \OT1/pcr/m/n/10.95 C \OT1/ptm/m/n/10.95 sat-is-fies \OT
1/pcr/m/n/10.95 IsGreensDClass \OT1/ptm/m/n/10.95 (\OT1/ptm/b/n/10.95 Reference
: Is-Greens-D-Class\OT1/ptm/m/n/10.95 ), then \OT1/pcr/m/n/10.95 GreensDClassDa
ta
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\OT1/ptm/m/n/10.95 re-turns an ob-ject in the cat-e-gory \OT1/pcr/m/n/10.95 IsG
reensDClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]) with rep-re-sen-ta-tion
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[30]
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[]\OT1/ptm/m/n/10.95 returns \OT1/pcr/m/n/10.95 true \OT1/ptm/m/n/10.95 if \OT1
/pcr/m/n/10.95 obj \OT1/ptm/m/n/10.95 lies in the cat-e-gory \OT1/pcr/m/n/10.95
 IsGreensData\OT1/ptm/m/n/10.95 , \OT1/pcr/m/n/10.95 IsGreensRClassData\OT1/ptm
/m/n/10.95 ,
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\OT1/pcr/m/n/10.95 IsGreensLClassData\OT1/ptm/m/n/10.95 , \OT1/pcr/m/n/10.95 Is
GreensHClassData\OT1/ptm/m/n/10.95 , \OT1/pcr/m/n/10.95 IsGreensDClassData\OT1/
ptm/m/n/10.95 , re-spec-tively. The ob-
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\OT1/ptm/m/n/10.95 and \OT1/pcr/m/n/10.95 DClassData \OT1/ptm/m/n/10.95 ([][]4.
2.7[][]) lie in the cat-e-gories \OT1/pcr/m/n/10.95 IsGreensRClassData\OT1/ptm/
m/n/10.95 , \OT1/pcr/m/n/10.95 IsGreensLClassData\OT1/ptm/m/n/10.95 ,
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[]\OT1/ptm/m/n/10.95 These func-tion con-struct ob-jects in the cat-e-gories \O
T1/pcr/m/n/10.95 IsGreensRClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]),
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\OT1/ptm/m/n/10.95 sub-cat-e-gories of \OT1/pcr/m/n/10.95 IsGreensData \OT1/ptm
/m/n/10.95 ([][]4.2.6[][]) us-ing the out-put from \OT1/pcr/m/n/10.95 GreensRCl
assData \OT1/ptm/m/n/10.95 ([][]4.2.2[][]),
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[]\OT1/ptm/m/n/10.95 returns \OT1/pcr/m/n/10.95 true \OT1/ptm/m/n/10.95 if \OT1
/pcr/m/n/10.95 obj \OT1/ptm/m/n/10.95 has \OT1/pcr/m/n/10.95 IsGreensRClassData
Rep\OT1/ptm/m/n/10.95 , \OT1/pcr/m/n/10.95 IsGreensLClassDataRep\OT1/ptm/m/n/10
.95 ,
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[31]
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[]\OT1/ptm/m/n/10.95 if \OT1/pcr/m/n/10.95 D \OT1/ptm/m/n/10.95 sat-is-fies \OT
1/pcr/m/n/10.95 IsGreensRClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]), \OT1/pcr
/m/n/10.95 IsGreensLClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]),
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\OT1/pcr/m/n/10.95 IsGreensHClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]), or \O
T1/pcr/m/n/10.95 IsGreensDClassData \OT1/ptm/m/n/10.95 ([][]4.2.6[][]), then \O
T1/pcr/m/n/10.95 SchutzenbergerGroup
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[32]
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[33]
Chapter 5.
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[40] [41]
Chapter 6.

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[42

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[46]
Chapter 7.
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[]\OT1/pcr/m/n/10.95 AutomorphismGroup \OT1/ptm/m/n/10.95 ([][]7.4.1[][]) with 
ar-gu-ment sat-is-fy-ing \OT1/pcr/m/n/10.95 IsTransformationSemigroup
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[]\OT1/pcr/m/n/10.95 IsomorphismSemigroups \OT1/ptm/m/n/10.95 ([][]7.7.5[][]) w
ith both ar-gu-ments sat-is-fy-ing
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[47

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[]\OT1/ptm/m/n/10.95 returns a semi-group ho-mo-mor-phism with rep-re-sen-ta-ti
on \OT1/pcr/m/n/10.95 IsSemigroupHomomorphismByFunctionRep
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[48]
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[]\OT1/ptm/m/n/10.95 returns a semi-group ho-mo-mor-phism with rep-re-sen-ta-ti
on \OT1/pcr/m/n/10.95 IsSemigroupHomomorphismByImagesOfGensRep
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[]\OT1/ptm/m/n/10.95 returns a semi-group ho-mo-mor-phism with rep-re-sen-ta-ti
on \OT1/pcr/m/n/10.95 IsSemigroupHomomorphismByImagesRep
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[49]
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[]\OT1/ptm/m/n/10.95 returns \OT1/pcr/m/n/10.95 true \OT1/ptm/m/n/10.95 if the 
gen-eral map-ping \OT1/pcr/m/n/10.95 f \OT1/ptm/m/n/10.95 is an in-ner au-to-mo
r-phism of a semi-group; see
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[50]
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[51]
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[]\OT1/ptm/m/n/10.95 If \OT1/pcr/m/n/10.95 autgroup \OT1/ptm/m/n/10.95 sat-is-f
ies \OT1/pcr/m/n/10.95 IsAutomorphismGroupOfZeroGroup \OT1/ptm/m/n/10.95 ([][]7
.4.5[][]), then
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\OT1/pcr/m/n/10.95 InnerAutomorphismsAutomorphismGroup \OT1/ptm/m/n/10.95 re-tu
rns the sub-group of in-ner au-to-mor-phisms in-
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[52]
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[]\OT1/ptm/m/sc/10.95 Please note: \OT1/ptm/m/n/10.95 if \OT1/phv/m/n/10.95 gra
pe \OT1/ptm/m/n/10.95 is not loaded, then this func-tion will not work when \OT
1/pcr/m/n/10.95 S
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\OT1/ptm/m/n/10.95 sat-is-fies \OT1/pcr/m/n/10.95 IsTransformationSemigroup \OT
1/ptm/m/n/10.95 (\OT1/ptm/b/n/10.95 Reference: Is-Trans-for-ma-tion-Semi-group\
OT1/ptm/m/n/10.95 ) or
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[54]
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[]\OT1/pcr/m/n/10.95 AutomorphismsSemigroupInGroup \OT1/ptm/m/n/10.95 re-turns 
the group of au-to-mor-phisms of the trans-for-
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\OT1/ptm/m/n/10.95 ma-tion semi-group \OT1/pcr/m/n/10.95 S \OT1/ptm/m/n/10.95 t
hat also be-long to the group \OT1/pcr/m/n/10.95 G\OT1/ptm/m/n/10.95 . If the v
alue of \OT1/pcr/m/n/10.95 G \OT1/ptm/m/n/10.95 is \OT1/pcr/m/n/10.95 fail\OT1/
ptm/m/n/10.95 , then
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[55]
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\OT1/ptm/m/sc/10.95 Please note: \OT1/ptm/m/n/10.95 if \OT1/phv/m/n/10.95 grape
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pcr/m/n/10.95 S \OT1/ptm/m/n/10.95 sat-
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\OT1/ptm/m/n/10.95 is-fies \OT1/pcr/m/n/10.95 IsTransformationSemigroup \OT1/pt
m/m/n/10.95 (\OT1/ptm/b/n/10.95 Reference: Is-Trans-for-ma-tion-Semi-group\OT1/
ptm/m/n/10.95 ) or
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[]\OT1/ptm/m/n/10.95 returns \OT1/pcr/m/n/10.95 true \OT1/ptm/m/n/10.95 if the 
ob-ject \OT1/pcr/m/n/10.95 f \OT1/ptm/m/n/10.95 is rep-re-sented as an au-to-mo
r-phism of a zero group; see
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[]\OT1/ptm/m/n/10.95 if \OT1/pcr/m/n/10.95 G \OT1/ptm/m/n/10.95 is the au-to-mo
r-phism group of a sim-ple trans-for-ma-tion semi-group, then
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\OT1/pcr/m/n/10.95 IsomorphismAutomorphismGroupOfRMS \OT1/ptm/m/n/10.95 re-turn
s a \OT1/pcr/m/n/10.95 GroupHomomorphismByImages \OT1/ptm/m/n/10.95 (\OT1/ptm/b
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\OT1/ptm/m/n/10.95 re-turns an iso-mor-phism from \OT1/pcr/m/n/10.95 G \OT1/ptm
/m/n/10.95 to a per-mu-ta-tion group by com-pos-ing the re-sult \OT1/pcr/m/n/10
.95 f \OT1/ptm/m/n/10.95 of
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[]\OT1/ptm/m/n/10.95 if \OT1/pcr/m/n/10.95 G \OT1/ptm/m/n/10.95 is a trans-for-
ma-tion semi-group that sat-is-fies \OT1/pcr/m/n/10.95 IsGroupAsSemigroup \OT1/
ptm/m/n/10.95 ([][]5.2.3[][]), then
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[]\OT1/ptm/m/n/10.95 returns an iso-mor-phism to a finitely pre-sented semi-gro
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[]\OT1/ptm/m/n/10.95 If \OT1/pcr/m/n/10.95 S \OT1/ptm/m/n/10.95 sat-is-fies \OT
1/pcr/m/n/10.95 IsSemigroup \OT1/ptm/m/n/10.95 (\OT1/ptm/b/n/10.95 Reference: I
s-Semi-group\OT1/ptm/m/n/10.95 ), use the com-mand
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[]\OT1/ptm/m/n/10.95 G. Kudryavt-seva and V. Ma-zorchuk.  On kisel-man's semi-g
roup.  2005.
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[]\OT1/pcr/m/n/10.95 ConjugatorOfInnerAutomorphismOfSemigroup\OT1/ptm/m/n/10.95
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[]\OT1/pcr/m/n/10.95 InnerAutomorphismsOfSemigroupInGroup\OT1/ptm/m/n/10.95 ,
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[]\OT1/pcr/m/n/10.95 IsomorphismReesMatrixSemigroupOfDClass\OT1/ptm/m/n/10.95 ,

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[]\OT1/pcr/m/n/10.95 SemigroupHomomorphismByImagesOfGensNC\OT1/ptm/m/n/10.95 ,
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