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

@article{Naik2019OnTP,
title={On the probability distribution associated to commutator word map in finite groups},
author={Tushar Kanta Naik},
journal={Communications in Algebra},
year={2019},
volume={47},
pages={3808 - 3817}
}
Abstract Let P(G) denotes the set of sizes of fibers of nontrivial commutators of the commutator word map. Here, we prove that , for any finite group G of nilpotency class 3 with exactly two conjugacy class sizes. We also show that for given , there exists a finite group G of nilpotency class 2 with exactly two conjugacy class sizes such that .
1 Citations
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Let $w$ be a word in $k$ variables. For a finite nilpotent group $G$, a conjecture of Amit states that $N_w(1) \ge |G|^{k-1}$, where $N_w(1)$ is the number of $k$-tuples $(g_1,...,g_k)\in G^{(k)}$Expand

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