Geodesic
Products of subgroups, subnormality, and relative orders of elements
Ars Mathematica Contemporanea, Tome 24 (2024) no. 1, article no. 09, 9 p.

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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|?
DOI : 10.26493/1855-3974.2975.1b2
Keywords: Relative exponents, products of subgroups, subnormal subgroups 
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Luca Sabatini. Products of subgroups, subnormality, and relative orders of elements. Ars Mathematica Contemporanea, Tome 24 (2024) no. 1, article  no. 09, 9 p. doi : 10.26493/1855-3974.2975.1b2. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2975.1b2/

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