We prove that a finite group G occurs as a maximal proper subsemigroup of an infinite semigroup (in the terminology of Freese, Je?ek, and Nation, G is a big semigroup) if and only if {pipe}G{pipe} ≥ 3. In fact, any finite semigroup whose minimal ideal contains a subgroup with at least three elements is big.
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机译：我们证明，当且仅当{pipe} G {pipe}≥3时，有限群G才能作为无限半群的最大适当子半群出现（在Freese，Jeekek和Nation的术语中，G是一个大半群）。实际上，其最小理想包含至少三个元素的子群的任何有限半群都是大的。
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