This article is cited in 4 papers

Mathematical logic, algebra and number theory

On $p$-complements of finite groups

A. A. Buturlakin^ab, D. O. Revin<sup>ab

a</sup> Sobolev Institute of Mathematics, 4 Acad. Koptyug avenue, 630090, Novosibirsk, Russia
^b Novosibirsk State University, 2 Pirogova Str., 630090, Novosibirsk, Russia

Abstract: A subgroup $H$ of a finite group $G$ is called a $p$-complement for a prime $p$, if the order of $H$ is not divided by $p$ and the index $|G:H|$ is a power of $p$. We give examples of a finite group that possesses two nonisomorphic $p$-complements and of a finite group in which all $p$-complements are isomorphic but not conjugate in the automorphism group.

Keywords: finite group, $p$-complement.

UDC: 512.542

MSC: 20D20

Received March 14, 2013, published May 6, 2013

Language: English