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On the structure of cancellative conjugation semigroups

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Abstract

As an abstraction of the conjugation on the multiplicative semigroup of quaternions, Garrão, Martins-Ferreira, Raposo, and Sobral (Semigroup Forum 100:806–836, 2020) introduced the notion of a conjugation semigroup, and studied the category of cancellative conjugation semigroups. In this note the conjugations of a group are shown to be in one-to-one correspondence with the endomorphisms of the group whose ranges are in the center. Moreover, cancellative conjugation semigroups are proved to be, up to isomorphism, the conjugation subsemigroups of conjugation groups.

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References

  1. Clifford, A.H., Preston, G.B.: The Algebraic Theory of Semigroups, Vol. I, Mathematical Surveys No. 7. American Mathematical Society, Providence, R.I. (1961)

  2. Garrão, A.P., Martins-Ferreira, N., Raposo, M., Sobral, M.: Cancellative conjugation semigroups and monoids. Semigroup Forum 100, 806–836 (2020)

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Correspondence to Mária B. Szendrei.

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Communicated by László Márki.

Dedicated to Richárd Wiegandt on his 90th birthday.

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The author was partially supported by the National Research, Development and Innovation Office (Hungary), Grants K115518 and K128042.

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Szendrei, M.B. On the structure of cancellative conjugation semigroups. Semigroup Forum 104, 724–730 (2022). https://doi.org/10.1007/s00233-022-10279-1

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  • DOI: https://doi.org/10.1007/s00233-022-10279-1

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