Omega subgroups of powerful p-groups
Gustavo A. Fern\'andez-Alcober

TL;DR
This paper provides elementary proofs for properties of omega subgroups in powerful finite p-groups, relating their exponents and element orders to subgroup indices, for all primes p.
Contribution
It offers a simplified, elementary proof of key properties of omega subgroups in powerful p-groups, extending understanding of their structure.
Findings
Exponent bounds for omega subgroups are established.
The subgroup index equals the count of elements with bounded order.
Results hold uniformly for all primes p.
Abstract
Let G be a powerful finite p-group. In this note, we give a short elementary proof of the following facts for all : (i) for odd p, and for p = 2; (ii) the index coincides with the number of elements of G of order at most .
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.
