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arXiv · 1502.06840

Maximal subgroups of finite soluble groups in general position

Eloisa Detomi·Andrea Lucchini
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Abstract

For a finite group $G$ we investigate the difference between the maximum size MaxDim$(G)$ of an "independent" family of maximal subgroups of $G$ and maximum size $m(G)$ of an irredundant sequence of generators of $G$. We prove that MaxDim$(G)=m(G)$ if the derived subgroup of $G$ is nilpotent. However MaxDim$(G)-m(G)$ can be arbitrarily large: for any odd prime $p,$ we construct a finite soluble group with Fitting length 2 satisfying $m(G)=3$ and MaxDim$(G)=p.$

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Eloisa Detomi, Andrea Lucchini. 2015-02-24. Maximal subgroups of finite soluble groups in general position. https://arxiv.org/abs/1502.06840

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