Products of Subgroups, Subnormality, and Relative Orders of Elements

Sabatini, Luca (2024) Products of Subgroups, Subnormality, and Relative Orders of Elements. ARS MATHEMATICA CONTEMPORANEA, 24 (1). pp. 1-9. ISSN 1855-3966 (print); 1855-3974 (online)

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Abstract

Let G be a group. We give an explicit description of the set of elements x ∈ G such that x|G:H| ∈ H for every subgroup of finite index H ≤ G. This is related to the following problem: given two subgroups H and K, with H of finite index, when does |HK : H| divide |G : H|?

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