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Cosets of normal subgroups and powers of conjugacy classes
Mathematische Nachrichten ( IF 0.8 ) Pub Date : 2021-08-03 , DOI: 10.1002/mana.201900554
Antonio Beltrán 1 , María José Felipe 2
Affiliation  

Let G be a finite group and let K = x G be the conjugacy class of an element x of G. In this paper, it is proved that if N is a normal subgroup of G such that the coset x N is the union of K and K 1 (the conjugacy class of the inverse of x), then N and the subgroup K are solvable. As an application, we prove that if there exists a natural number n 2 such that K n = K K 1 , then K is solvable.

中文翻译:

正常子群的陪集和共轭类的幂

G是一个有限群,令 = X G 是共轭类的元素的XG ^。本文证明,若NG的正规子群,则陪集 X N K - 1 x的逆的共轭类),然后N和子群 是可以解决的。作为一个应用,我们证明如果存在一个自然数 n 2 以至于 n = - 1 , 然后 是可以解决的。
更新日期:2021-08-03
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