arxiv:2412.12345

Critical groups and partitions of finite groups

Published on Dec 16, 2024

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Abstract

The study investigates finite groups based on properties of power graph closed twins and provides results on groups that can be partitioned into cyclic subgroups.

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We define a class of finite groups based on the properties of the closed twins of their power graphs and study the structure of those groups. As a byproduct, we obtain results about finite groups admitting a partition by cyclic subgroups.

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