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
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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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