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In the name of God

Dear Gap Forum,

Hello to all

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 $|R|\leq n^2$?

Thank you very much in advance for any help from you.

Sincerely Yours

Alireza Abdollahi

=====

Alireza Abdollahi

Department of Mathematics

University of Isfahan,

Isfahan 81744,Iran

e-mail: alireza_abdollahi@yahoo.com

URL: http://www.abdollahi.8m.net

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