2024/01/21 by O. Al Raisi, Raisi, O. Al, M. Shahryari +1
Mathematics · #Rings, Modules, and Algebras #Advanced Topology and Set Theory #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.2401.11397
A group is CSA, if all of its maximal abelian subgroups are malnormal. It is known that every non-abelian CSA group is an equational domain. We generalize this result in two directions: we show that for a non-nilpotent group G and a fixed positive integer k, if all maximal elements in the set of class k nilpotent subgroups of G are malnormal, then G is an equational domain. Also, we prove that if a group G is not locally nilpotent and if every maximal locally nilpotent subgroup of G is malnormal, then G is an equational domain.