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Dear Alireza Abdollahi, dear GAP Forum,

Last Friday you wrote to the GAP Forum:

I have encountered to the following question:

Let $n>3$ be a postive integer and let $G=RX$ be an extention of an elementary abelian $p$-group by an abelian $p'$-subgroup $X$ such that $X$ acts faithfully on $R$ and $R=[R,X]$ and $|[R,x]|\leq n$ for all $x\in X$. It can be proved that $|X|\leq n-1$ and $|R|\leq n^{\log_2(n-2)}$. Is it true that $|R|\leq n^2$?

I am sorry that I have no idea how to answer your question, but since

nobody from the GAP Forum has reacted as yet, the colleagues reading

the GAP Forum seem not to have an answer either.

However for a theoretical question such as the one you ask, the GAP

Forum is perhaps not the right address. The GAP Forum is meant for

discussing questions related to the use of GAP, but in the case of

your question the only chance to use GAP would be if somebody had an

idea for a possible counterexample and would then use GAP to verify

it.

Rather I want to suggest to send your question - as well as similarly

'theoretical' questions - to the 'group-pub-forum' maintained by Geoff

Smith at Bath, UK, that is read by many group theoreticians, not only

those who are interested in GAP.

With kind regards Joachim Neubueser

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