Shubham MITTAL, Gaurav MITTAL, R. K. SHARMA

A note on Friendly and Solitary Groups

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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