Products of subgroups, subnormality, and relative orders of elements
- Resource Type
- Working Paper
- Authors
- Sabatini, Luca
- Source
- Ars Math. Contemp. (2023)
- Subject
- Mathematics - Group Theory
20D40, 20D25, 20F99
- Language
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 $|G:H|$?
Comment: 8 pages