On the Length of a Maximal Subgroup of a Finite Group

2025/03/31 by Viachaslau I. Murashka, Murashka, Viachaslau I., А. Ф. Васильев +1
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2503.24335

openalex publication_date 2025/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a finite group G and its maximal subgroup M we proved that the generalized Fitting height of M can't be less by 2 than the generalized Fitting height of G and the non-p-soluble length of M can't be less by 1 than the non-p-soluble length of G. We constructed a hereditary saturated formation \mathfrakF such that \n_σ(G, \mathfrakF)-n_σ(M, \mathfrakF)| G is finite σ-soluble and M is a maximal subgroup of G\=ℕ∪\0\ where n_σ(G, \mathfrakF) denotes the σ-nilpotent length of the \mathfrakF-residual of G. This construction shows the results about the generalized lengths of maximal subgroups published in Math. Nachr. (1994) and Mathematics (2020) are not correct.

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