Minimal non-Iwasawa finite groups
Marius T\u{a}rn\u{a}uceanu

TL;DR
This paper characterizes minimal non-Iwasawa finite groups, explores their modular cases, and investigates their subgroup commutativity degrees, including a family of non-nilpotent examples with degrees approaching one.
Contribution
It provides a detailed structure of minimal non-Iwasawa finite groups and links them to subgroup commutativity degrees, including new examples with specific properties.
Findings
Classification of minimal non-Iwasawa finite groups
Identification of modular minimal non-Iwasawa groups
Construction of a family with subgroup commutativity degree approaching 1
Abstract
In this note, we describe first the structure of minimal non-Iwasawa finite groups. Then we determine the minimal non-Iwasawa finite groups which are modular. Also, we find connections between minimal non-Iwasawa finite groups and the subgroup commutativity degree, and we give an example of a family of non-nilpotent modular finite groups , , whose subgroup commutativity degree tends to as tends to infinity.
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