Products of subgroups, subnormality, and relative orders of elements
Luca Sabatini

TL;DR
This paper characterizes elements in a group based on their powers relative to subgroups of finite index and explores conditions under which subgroup products have orders dividing certain group indices.
Contribution
It provides an explicit description of elements satisfying specific power conditions related to finite index subgroups and investigates divisibility properties of subgroup products.
Findings
Explicit description of elements with $x^{|G:H|} \
Conditions for divisibility of subgroup product orders by group indices
Connections between element powers and subgroup normality
Abstract
Let be a group. We give an explicit description of the set of elements such that for every subgroup of finite index . This is related to the following problem: given two subgroups and , with of finite index, when does divide ?
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFinite Group Theory Research · Graph theory and applications · graph theory and CDMA systems
