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Question: Three questions on groups

Question:Three questions on groups

ComputerUser 535 Maple
group-theory
July 05 2015
0

1.

similar gap system, which function can output coset table ?

if find example below,

f := FreeGroup( "a", "b" );

g := f / [f.1^2, f.2^3, (f.1*f.2)^5];
tab := CosetTable(g, Subgroup(g, [g.1, g.2*g.1*g.2*g.1*g.2^-1]));

 

2.

if quotient group is for equivalence relations, what do relations [g.1, g.2*g.1*g.2*g.1*g.2^-1] for? which kind of relations is for input to subgroup parameter which is like relations?

 

3. equalivance relations in wiki mentioned is to partition cells, how do they satisfy symmetric, reflexive and transitive after partition? how to test these partition?
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