[GAP Forum] Manual Proof of GAP Results on Generators of Factor Groups

[Minghui Liu]

Dear GAP Forum,

I am trying to find generators of a factor group. I have input dozens
of generators and relations and when I use the command

AbelianInvariants(F/relations);

the result was something like

0, 0, 0, 0, 0, 0, 0, 2, 5.

After finding that the image of some generator, say F.1*F.2^5*F.3^3 has
order 5 in the quotient group F/relations, is there any way we can manually
write a proof that the order of the image of F.1*F.2^5*F.3^3 is equal to 5,
perhaps with the help of GAP?

My point is, instead of writing "by calculation based on GAP, we have the
order is equal to 5", it would be desirable to find a algebraic proof of
the result. Anyone knows how it can be done?

Any assistance will be greatly appreciated.

Best regards,

Minghui