Non-virtually nilpotent groups have infinite conjugacy class quotients

2018/03/13 by Joshua Frisch, Frisch, Joshua, Pooya Vahidi Ferdowsi +1 · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1803.05064

openalex publication_date 2018/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We offer in this note a self-contained proof of the fact that a finitely generated group is not virtually nilpotent if and only if it has a quotient with the infinite conjugacy class (ICC) propoerty. This proof is a modern presentation of the original proof, by McLain (1956) and Duguid and McLain (1956).

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