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<p>The monoid of non-empty subsets of a group, with respect to the natural multiplication of subsets, is called the power semigroup of the group. We prove that every semigroup embeds in the power semigroup of a free group, while not every semigroup—even a periodic one—is embeddable in the power semigroup of a periodic group. We provide some necessary and some sufficient conditions for the embeddability in the power semigroup of a periodic group.</p>

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On power semigroups of groups

  • 期刊论文

  • 发表日期：

    2025年11月18日

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  • S. G. Bershadsky,
  • S. I. Kublanovsky

摘要

The monoid of non-empty subsets of a group, with respect to the natural multiplication of subsets, is called the power semigroup of the group. We prove that every semigroup embeds in the power semigroup of a free group, while not every semigroup—even a periodic one—is embeddable in the power semigroup of a periodic group. We provide some necessary and some sufficient conditions for the embeddability in the power semigroup of a periodic group.