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<p>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 prove that this result can be generalized in two directions: we show that for a non-nilpotent group <i>G</i> and a fixed positive integer <i>k</i>, if all maximal class <i>k</i> nilpotent subgroups of <i>G</i> are malnormal, then <i>G</i> is an equational domain. Also, we prove that if a group <i>G</i> is not locally nilpotent and if every maximal locally nilpotent subgroup of <i>G</i> is malnormal, then <i>G</i> is an equational domain.</p>

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New Classes of Groups Which are Equational Domains

  • 期刊论文

  • 发表日期：

    2025年4月21日

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  • Omar Al-Raisi,
  • Mohammad Shahryari

摘要

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 prove that this result can be generalized in two directions: we show that for a non-nilpotent group G and a fixed positive integer k, if all maximal 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.