Year: 2026
Type: article
Abstract: A.R. Camina and R.D. Camina posed the following question: Suppose there are two finite groups, one nilpotent and the other non-nilpotent, and the two groups share identical sets of conjugacy class sizes; must the non-nilpotent group possess a non-trivial center? Recently, W. Zhou gave a negative answer via a subtle and elegant construction of concrete counterexamples. Nevertheless, his approach relies on the existence of Sophie Germain primes, and thus fails to yield infinitely many counterexamples unconditionally. In the present paper, we construct an infinite family of counterexamples to Camina’s question.
Author: Yu Zeng
Institution: Twitter (United States)
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166183402
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