منابع مشابه
THE DERIVED SERIES OF A FINITE p-GROUP
Let G be a finite p-group, and let G denote the d-th term of the derived series of G . We show, for p > 5, that G 6= 1 implies logp |G | > 2 d + 3d − 6, and hence we improve a recent result by Mann.
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Let $G$ be a $p$-group of nilpotency class $k$ with finite exponent $exp(G)$ and let $m=lfloorlog_pk floor$. We show that $exp(M^{(c)}(G))$ divides $exp(G)p^{m(k-1)}$, for all $cgeq1$, where $M^{(c)}(G)$ denotes the c-nilpotent multiplier of $G$. This implies that $exp( M(G))$ divides $exp(G)$, for all finite $p$-groups of class at most $p-1$. Moreover, we show that our result is an improvement...
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Every Seifert Fibre Group is the lift of a Fuchsian group to the universal covering group of PSL (2,R). From this, we work out a form of presentation for such a group. With the calculation of the Euler number, we can establish the presentation of the derived group of a Seifert Fibre Group
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Many common finite p-groups admit automorphisms of order coprime to p, and when p is odd, it is reasonably difficult to find finite p-groups whose automorphism group is a p-group. Yet the goal of this paper is to prove that the automorphism group of a finite p-group is almost always a p-group. The asymptotics in our theorem involve fixing any two of the following parameters and letting the thir...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1961
ISSN: 0019-2082
DOI: 10.1215/ijm/1255629822