[GAP Forum] An issue with finitely presented groups

[Dr. Kashyap Rajeevsarathy]

 Dear Forum,

I was trying to ascertain the membership of a word (in this case a letter
b2) in the index 2 subgroup of a finitely presented (surface) group. Please
point me to a better alternative (if possible) to the example below:


gap> f := FreeGroup("a1","b1","a2","b2");

<free group on the generators [ a1, b1, a2, b2 ]>

gap> genf := GeneratorsOfGroup(f);

[ a1, b1, a2, b2 ]

gap> G :=
f/[genf[1]*genf[2]*genf[1]^(-1)*genf[2]^(-1)*genf[3]*genf[4]*genf[3]^(-1)*genf[4]^(-1)];


<fp group of size infinity on the generators [ a1, b1, a2, b2 ]>

gap> genG := GeneratorsOfGroup(G);

[ a1, b1, a2, b2 ]

gap> H := Subgroup(G,[genG[1],genG[2],genG[3],genG[4]^2]);

Group([ a1, b1, a2, b2^2 ])

gap> genH := GeneratorsOfGroup(H);

[ a1, b1, a2, b2^2 ]

gap> genG[4] in H;

Error, the coset enumeration has defined more than 4096000 cosets

 called from

TCENUM.CosetTableFromGensAndRels( fgens, grels, fsgens ) called from

CosetTableFromGensAndRels( fgens, grels, fsgens ) called from

TryCosetTableInWholeGroup( H ) called from

CosetTableInWholeGroup( U ) called from

<function "unknown">( <arguments> )

 called from read-eval loop at line 8 of *stdin*

type 'return;' if you want to continue with a new limit of 8192000 cosets,

type 'quit;' if you want to quit the coset enumeration,

type 'maxlimit := 0; return;' in order to continue without a limit

brk>

Thanks,
Kashyap

-- 
Kashyap Rajeevsarathy
Assistant Professor,
Indian Institute of Science Education and Research (IISER) Bhopal,
Indore By-pass Road,
Bhauri, Bhopal - 462066,
Madhya Pradesh, India.
Phone: +91-755-669-1273
Website: https://home.iiserb.ac.in/~kashyap