On the probability distribution associated to commutator word map in finite groups \rom2

2018/04/30 by Tushar Kanta Naik, Naik, Tushar Kanta
Computer Science · Mathematics · #20D60 #20P05 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1805.00091

openalex publication_date 2018/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let P(G) denotes the set of sizes of fibers of non-trivial commutators of the commutator word map. Here, we prove that |P(G)|=1, for any finite group G of nilpotency class 3 with exactlly two conjugacy class sizes. We also show that for given n≥ 1, there exists a finite group G of nilpotency class 2 with exactlly two conjugacy class sizes such that |P(G)|=n.

Related

• The Probability Distribution of Word Maps on Finite Groups
• Enumerating fibres of commutator words over p-groups
• Words, permutations, and the nonsolvable length of a finite group
• On the probability of satisfying a word in nilpotent groups of class 2
• Commuting probability and simultaneous conjugacy classes of commuting tuples in a group