Year: 2026
Type: preprint
Abstract: Let $P$ be a finite metacyclic $p$-group where $p$ is an odd prime. We refine the notions split metacyclic and non-split metacyclic group by distinguishing whether a metacyclic structure (i.e. a cyclic normal subgroup $K$ of $P$ such that $P/K$ is also cyclic) is non-splittable or splittable or automatically split. We show that these different types can be characterised in terms of $|K|$. We also determine which of these types can coexist on the same group $P$.
Source: arXiv (Cornell University)
Author: Schweizer, Andreas
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G337935221
OpenAlex ID: W7204185175
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