ON FINITE GROUPS WHOSE DERIVED SUBGROUP HAS BOUNDED RANK K. PODOSKI and B. SZEGEDY
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چکیده
Let G be a finite group with derived subgroup of rank r. We prove that |G : Z2(G)| ≤ |G |. Motivated by the results of I. M. Isaacs in [2] we show that if G is capable then |G : Z(G)| ≤ |G| . This answers a question of L. Pyber. We prove that if G is a capable p-group then the rank of G/Z(G) is bounded above in terms of the rank of G′.
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تاریخ انتشار 2008