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Question: How to find a permutation group with generator and relation

Question:How to find a permutation group with generator and relation

ComputerUser 535
group-theory
July 06 2013
1

 

a,b ; a^2, b^2, a*b = b*a

is a presentation

a and b are permutation group

a*b = b*a is relation

i am not sure a^2 or b^2 are generator, i guess they are

so how to find a and b which are permutation group?

 

is it a,b ; a^2, b^2, a*b = b*a     or      a,b ; a^2=1, b^2=1, a*b = b*a  ?

 

if a^2, b^2, a*b = b*a , i do not know what is a^2 if a^2 = 1

 

so i guess and prefer  a,b ; a^2=1, b^2=1, a*b = b*a 

 

then i guess that i have to find a and b which can be simple integer matrix which fits relation

however the goal is to find permutation group
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