A note on Friendly and Solitary Groups

Year 2023, , 197 - 206, 10.07.2023

Shubham Mıttal Gaurav Mıttal R. K. Sharma

https://doi.org/10.24330/ieja.1260499

Abstract

In this paper, we extend the notions of friendly and solitary
numbers to group theory and define friendly and solitary groups of
type-1 and type-2. We provide many examples of friendly and
solitary groups and study certain properties of the type-2 friends
of cyclic $p$-groups, where $p$ is a prime number.

Keywords

Group, $p$-group, number theory

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