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A Note on Relative Normal Subgroups

Last modified: 2021-11-19

#### Abstract

Let

*G*be a group and a be an automorphism of*G*. In 2016, Ganjali and Erfanian introduced the notion of a normal subgroup of*G*which is relative to a, called an a-normal subgroup. Suppose that*N*is an a-normal subgroup of*G*. In this research, we show that*N*is t-normal in*G*for an automorphism t in*Aut*(*G*) if and only if a(g)t(g^{-1}) is in*N*for every*g*in*G*.a