Year: 2026
Type: preprint
Abstract: We investigate conditions under which a semidirect product $G=HN$, and in particular a restricted wreath product, is an equational domain. For a variety of groups $\X$, we study semidirect products of $\XT$-groups (groups where $\langle A, B\rangle \in\X$ for any two $\X$-subgroups $A$ and $B$ with nontrivial intersection) and $\CSX$-groups (groups where all maximal $\X$-subgroups are malnormal). We pay particular attention to split Frobenius groups and investigate conditions under which such groups are $\XT$- or $\CSX$-groups.
Source: arXiv (Cornell University)
Authors: Al-Raisi, Omar, Shahryari, Mohammad
Institution: Sultan Qaboos University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223667242