On the probability distribution associated to commutator word map in finite groups \rom{2}
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 $n\geq 1$, there exists a finite group $G$ of nilpotency class $2$ with exactlly two conjugacy class sizes such that $|P(G)|=n$.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2018
- DOI:
- 10.48550/arXiv.1805.00091
- arXiv:
- arXiv:1805.00091
- Bibcode:
- 2018arXiv180500091K
- Keywords:
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- Mathematics - Group Theory;
- 20D60;
- 20P05
- E-Print:
- Minor correction in Lemma 2.6 and added one more lemma