Talk:Epigroup
Add topicLatest comment: 2 years ago by Trevori in topic Subsemigroups of epigroups need not be subepigroups?
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Subsemigroups of epigroups need not be subepigroups?
[edit]Let S be a subsemigroup of an epigroup E and pick any element x in S. It has a power x^k that is an element of a subgroup G with identity 1_G. Then x^w = 1_G for some w, which is in S. The set {x^w,...,x^{2w-1}} is then a subgroup of S, proving that S is an epigroup. This paper, https://core.ac.uk/download/pdf/81983813.pdf, states that epigroups are "closed under forming substructures". Is the wikipedia article wrong? Trevori (talk) 20:23, 25 August 2023 (UTC)