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
Word problems for finite nilpotent groups
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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The probability distribution associated to the commutator word map is studied and explicit formulas for calculating this probability for some interesting classes of groups having only two different conjugacy class sizes are computed. Expand
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