Doaa Mustafa Alsharo, Hajar Sulaiman
School of Mathematical Sciences
Universiti Sains Malaysia
11800, USM, Penang, MALAYSIA
School of Mathematical Sciences
Universiti Sains Malaysia
11800, USM, Penang, MALAYSIA

Abstract. The permutability of subgroups in a finite group was recently discovered and a number of related results have been published. As there is a close relationship between permutability and normality, it is not surprising that a property called normality was defined and linked with permutability. By definition, all normal subgroups are permutable. In this paper, we show that the converse is not true by creating a group of order containing a permutable subgroup that is not normal.

Received: February 12, 2014

AMS Subject Classification: 20D10

Key Words and Phrases: permutable subgroups, c-normal subgroups, c-permutable subgroups

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