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arXiv · 2210.02261

Products of subgroups, subnormality, and relative orders of elements

Luca Sabatini
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Abstract

Let $G$ be a group. We give an explicit description of the set of elements $x \in G$ such that $x^{|G:H|} \in H$ for every subgroup of finite index $H \leqslant G$. 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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Luca Sabatini. 2022-10-05. Products of subgroups, subnormality, and relative orders of elements. https://doi.org/10.26493/1855-3974.2975.1b2

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