## File: perf.gd

package info (click to toggle)
gap 4r8p6-2
• area: main
• in suites: stretch
• size: 33,476 kB
• ctags: 7,663
• sloc: ansic: 108,841; xml: 47,807; sh: 3,628; perl: 2,342; makefile: 796; asm: 62; awk: 6
 file content (376 lines) | stat: -rw-r--r-- 13,047 bytes parent folder | download | duplicates (3)
 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376 ############################################################################# ## #W perf.gd GAP Groups Library Alexander Hulpke ## ## #Y Copyright (C) 1997, Lehrstuhl D für Mathematik, RWTH Aachen, Germany ## ## This file contains the declarations for the Holt/Plesken library of ## perfect groups ## PERFRec := fail; # indicator that perf0.grp is not loaded PERFSELECT := []; PERFGRP := []; ############################################################################# ## #C IsPerfectLibraryGroup() identifier for groups constructed from the ## library (used for perm->fp isomorphism) ## ## ## ## ## ## ## ## DeclareCategory("IsPerfectLibraryGroup", IsGroup ); ############################################################################# ## #O PerfGrpConst(,) ## ## ## ## ## ## ## ## DeclareConstructor("PerfGrpConst",[IsGroup,IsList]); ############################################################################# ## #F PerfGrpLoad() force loading of secondary files, return index ## ## ## ## ## ## ## ## DeclareGlobalFunction("PerfGrpLoad"); ############################################################################# ## #A PerfectIdentification() . . . . . . . . . . . . id. for perfect groups ## ## <#GAPDoc Label="PerfectIdentification"> ## ## ## ## ## This attribute is set for all groups obtained from the perfect groups ## library and has the value [size,nr] if the group is obtained with ## these parameters from the library. ## ## ## <#/GAPDoc> ## DeclareAttribute("PerfectIdentification", IsGroup ); ############################################################################# ## #F SizesPerfectGroups() ## ## <#GAPDoc Label="SizesPerfectGroups"> ## ## ## ## ## This is the ordered list of all numbers up to 10^6 that occur as ## sizes of perfect groups. ## One can iterate over the perfect groups library with: ## for n in SizesPerfectGroups() do ## > for k in [1..NrPerfectLibraryGroups(n)] do ## > pg := PerfectGroup(n,k); ## > od; ## > od; ## ]]> ## ## ## <#/GAPDoc> ## DeclareGlobalFunction("SizesPerfectGroups"); ############################################################################# ## #F NumberPerfectGroups( ) . . . . . . . . . . . . . . . . . . . . . . ## ## <#GAPDoc Label="NumberPerfectGroups"> ## ## ## ## ## returns the number of non-isomorphic perfect groups of size size for ## each positive integer size up to 10^6 except for the eight sizes ## listed at the beginning of this section for which the number is not ## yet known. For these values as well as for any argument out of range it ## returns fail. ## ## ## <#/GAPDoc> ## DeclareGlobalFunction("NumberPerfectGroups"); DeclareSynonym("NrPerfectGroups",NumberPerfectGroups); ############################################################################# ## #F NumberPerfectLibraryGroups( ) . . . . . . . . . . . . . . . . . . ## ## <#GAPDoc Label="NumberPerfectLibraryGroups"> ## ## ## ## ## returns the number of perfect groups of size size which are available ## in the library of finite perfect groups. (The purpose of the function ## is to provide a simple way to formulate a loop over all library groups ## of a given size.) ## ## ## <#/GAPDoc> ## DeclareGlobalFunction("NumberPerfectLibraryGroups"); DeclareSynonym("NrPerfectLibraryGroups",NumberPerfectLibraryGroups); ############################################################################# ## #F PerfectGroup( [, ][, ] ) #F PerfectGroup( [, ] ) ## ## <#GAPDoc Label="PerfectGroup"> ## ## PerfectGroup ## ## ## ## ## returns a group which is isomorphic to the library group specified ## by the size number [ size, n ] or by the two ## separate arguments size and n, assuming a default value of ## n = 1. ## The optional argument filt defines the filter in which the group is ## returned. ## Possible filters so far are and ## . ## In the latter case, the generators and relators used coincide with those ## given in . ## G := PerfectGroup(IsPermGroup,6048,1); ## U3(3) ## gap> G:=PerfectGroup(IsPermGroup,823080,2); ## A5 2^1 19^2 C 19^1 ## gap> NrMovedPoints(G); ## 6859 ## ]]> ## ## ## <#/GAPDoc> ## DeclareGlobalFunction("PerfectGroup"); ############################################################################# ## #F DisplayInformationPerfectGroups( [, ] ) . . . . . . . . . . . . #F DisplayInformationPerfectGroups( ] ) . . . . . . . . . . ## ## <#GAPDoc Label="DisplayInformationPerfectGroups"> ## ## DisplayInformationPerfectGroups ## ## ## ## ## ## displays some invariants of the n-th group of order size ## from the perfect groups library. ##

## If no value of n has been specified, the invariants will be ## displayed for all groups of size size available in the library. ##

## Alternatively, also a list of length two may be entered as the only ## argument, with entries size and n. ##

## The information provided for G includes the following items: ## ## ## a headline containing the size number [ size, n ] of G ## in the form size.n (the suffix .n will be suppressed ## if, up to isomorphism, G is the only perfect group of order ## size), ## ## ## a message if G is simple or quasisimple, i.e., ## if the factor group of G by its centre is simple, ## ## ## the description of the structure of G as it is ## given by Holt and Plesken in  (see below), ## ## ## the size of the centre of G (suppressed, if G is ## simple), ## ## ## the prime decomposition of the size of G, ## ## ## orbit sizes for a faithful permutation representation ## of G which is provided by the library (see below), ## ## ## a reference to each occurrence of G in the tables of ## section 5.3 of . Each of these references ## consists of a class number and an internal number (i,j) under which ## G is listed in that class. For some groups, there is more than one ## reference because these groups belong to more than one of the classes ## in the book. ## ## ## DisplayInformationPerfectGroups( 30720, 3 ); ## #I Perfect group 30720: A5 ( 2^4 E N 2^1 E 2^4 ) A ## #I size = 2^11*3*5 orbit size = 240 ## #I Holt-Plesken class 1 (9,3) ## gap> DisplayInformationPerfectGroups( 30720, 6 ); ## #I Perfect group 30720: A5 ( 2^4 x 2^4 ) C N 2^1 ## #I centre = 2 size = 2^11*3*5 orbit size = 384 ## #I Holt-Plesken class 1 (9,6) ## gap> DisplayInformationPerfectGroups( Factorial( 8 ) / 2 ); ## #I Perfect group 20160.1: A5 x L3(2) 2^1 ## #I centre = 2 size = 2^6*3^2*5*7 orbit sizes = 5 + 16 ## #I Holt-Plesken class 31 (1,1) (occurs also in class 32) ## #I Perfect group 20160.2: A5 2^1 x L3(2) ## #I centre = 2 size = 2^6*3^2*5*7 orbit sizes = 7 + 24 ## #I Holt-Plesken class 31 (1,2) (occurs also in class 32) ## #I Perfect group 20160.3: ( A5 x L3(2) ) 2^1 ## #I centre = 2 size = 2^6*3^2*5*7 orbit size = 192 ## #I Holt-Plesken class 31 (1,3) ## #I Perfect group 20160.4: simple group A8 ## #I size = 2^6*3^2*5*7 orbit size = 8 ## #I Holt-Plesken class 26 (0,1) ## #I Perfect group 20160.5: simple group L3(4) ## #I size = 2^6*3^2*5*7 orbit size = 21 ## #I Holt-Plesken class 27 (0,1) ## ]]> ## ## ## <#/GAPDoc> ## DeclareGlobalFunction("DisplayInformationPerfectGroups"); ############################################################################# ## #F SizeNumbersPerfectGroups( , , ... ) ## ## <#GAPDoc Label="SizeNumbersPerfectGroups"> ## ## ## ## ## returns a list of pairs, ## each entry consisting of a group order and the number of those groups in ## the library of perfect groups that contain the specified factors ## factor1, factor2, ... ## among their composition factors. ##

## Each argument must either be the name of a simple group or an integer ## which stands for the product of the sizes of one or more cyclic factors. ## (In fact, the function replaces all integers among the arguments ## by their product.) ##

## The following text strings are accepted as simple group names. ## ## ## An or A(n) for the alternating groups ## A_{n}, ## 5 \leq n \leq 9, for example A5 or A(6). ## ## ## Ln(q) or L(n,q) for ## PSL(n,q), where ## n \in \{ 2, 3 \} and q a prime power, ranging ## ## ## for n = 2 from 4 to 125 ## ## ## for n = 3 from 2 to 5 ## ## ## ## ## Un(q) or U(n,q) for ## PSU(n,q), where ## n \in \{ 3, 4 \} and q a prime power, ranging ## ## ## for n = 3 from 3 to 5 ## ## ## for n = 4 from 2 to 2 ## ## ## ## ## Sp4(4) or S(4,4) for the symplectic group Sp(4,4), ## ## ## Sz(8) for the Suzuki group Sz(8), ## ## ## Mn or M(n) for the Mathieu groups ## M_{11}, M_{12}, and M_{22}, and ## ## ## Jn or J(n) for the Janko groups ## J_1 and J_2. ## ## ##

## Note that, for most of the groups, the preceding list offers two ## different names in order to be consistent with the notation used in ## as well as with the notation used in the ## command of &GAP;. ## However, as the names are ## compared as text strings, you are restricted to the above choice. Even ## expressions like L2(2^5) are not accepted. ##

## As the use of the term PSU(n,q) is not unique in the literature, ## we mention that in this library it denotes the factor group of ## SU(n,q) by its centre, where SU(n,q) is the group of all ## n \times n unitary matrices with entries in GF(q^2) ## and determinant 1. ##

## The purpose of the function is to provide a simple way to formulate a ## loop over all library groups which contain certain composition factors. ## ## ## <#/GAPDoc> ## DeclareGlobalFunction("SizeNumbersPerfectGroups"); ############################################################################# ## #E