Finite groups with a certain number of elements pairwise generating a non-nilpotent subgroup

Details Finite groups with a certain number of elements pairwise generating a non-nilpotent subgroup Finite groups with a certain number of elements pairwise generating a non-nilpotent subgroup

2005-11-28

arxiv.org/abs/math/0511667v1

Mathematics

Group Theory

Published in Bulletin of the Iranian Mathematical Society, Vol. 30 No. 2 (2004), pp. 1-20

Scientific paper

Let $n>0$ be an integer and $\mathcal{X}$ be a class of groups. We say that a group $G$ satisfies the condition $(\mathcal{X},n)$ whenever in every subset with $n+1$ elements of $G$ there exist distinct elements $x,y$ such that $$ is in $\mathcal{X}$. Let $\mathcal{N}$ and $ \mathcal{A}$ be the classes of nilpotent groups and abelian groups, respectively. Here we prove that: (1) If $G$ is a finite semi-simple group satisfying the condition $(\mathcal{N},n)$, then $|G|

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