Enumerating classes and characters of p-groups
E. A. O'Brien, C. Voll

TL;DR
This paper develops formulas to count conjugacy classes and irreducible characters in finite p-groups of nilpotency class less than p, unifying and extending previous results using advanced algebraic tools.
Contribution
It introduces general formulas for enumeration in p-groups of certain classes, generalizing prior results with the Lazard correspondence and Kirillov orbit method.
Findings
Unified enumeration formulas for conjugacy classes and characters
Extended results to generalized relatively free p-groups
Applicable to p-groups of nilpotency class less than p
Abstract
We develop general formulae for the numbers of conjugacy classes and irreducible complex characters of finite p-groups of nilpotency class less than p. This allows us to unify and generalize a number of existing enumerative results, and to obtain new such results for generalizations of relatively free p-groups of exponent p. Our main tools are the Lazard correspondence and the Kirillov orbit method.
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 · Coding theory and cryptography · Advanced Algebra and Geometry
