Maximal subgroups of finite soluble groups in general position

2015/02/24 by Eloisa Detomi, Detomi, Eloisa, Andrea Lucchini +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #20F16 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Protein Tyrosine Phosphatases

paper · pdf · doi:10.48550/arxiv.1502.06840

openalex publication_date 2015/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On an Inequality of Dimension-like Invariants for Finite Groups

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