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CHARACTERIZING FINITE GROUPS WITH NORMAL $p$-SUBGROUPS FOR THE SMALLEST PRIME DIVISOR OF THE ORDER OF THE GROUP
Keywords:
Dedekind group, Hamiltonian group, p-subgroup, Sylow subgroupDOI:
https://doi.org/10.17654/0972555524014Abstract
This article studies the group-theoretic constraints on particular subgroups of a finite group. These constraints are established through the concept of normality, resulting in a new group description. In particular, we consider a finite group $G$ with $p$ being the smallest prime divisor of its order. When every $p$-subgroup is normal in $G$, we say that $G$ is a $pn$-group. In the current paper, we provide a characterization of all finite $pn$-groups and show their main properties.
Received: January 14, 2024
Revised: February 6, 2024
Accepted: March 5, 2024
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