A criterion for nilpotency in finite groups.

Autor: Li, Binbin, Lu, Jiakuan, Pang, Linna, Zhang, Boru
Zdroj: Archiv der Mathematik; Jan2024, Vol. 122 Issue 1, p13-16, 4p
Abstrakt: For a positive integer n, we denote by π (n) the set of prime divisors of n. For a group G and a ∈ G , we denote by o(a) the order of the element a. We prove that a finite group G is nilpotent if and only if π (o (a b)) = π (o (a) o (b)) for all a, b ∈ G of coprime orders. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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