Some Conditions that Turn a Certain Semigroup into a 
Group

Osman Hysa; Orgest Beqiri

doi:https://doi.org/10.14445/22315373/IJMTT-V71I3P105

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 71 | Issue 3 | Year 2025 | Article Id. IJMTT-V71I3P105 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I3P105

Some Conditions that Turn a Certain Semigroup into a Group

Osman Hysa, Orgest Beqiri

Received	Revised	Accepted	Published
11 Jan 2025	22 Feb 2025	12 Mar 2025	30 Mar 2025

Abstract

Semigroups are an important class of algebraic structures. One of the most important subclasses of semigroups are groups. There are some subclasses of semigroups that are ″close″ to groups, such as regular semigroups, orthodox semigroups and inverse semigroups. Finding conditions for semigroups that turn them into groups is interesting and important. In this paper, we give our original proofs of some propositions, which show how certain semigroups turn into groups, satisfying some conditions. Among other things, we give a counterexample to show that there is a cancellative and infinite semigroup, which is not a group.

Keywords

Semigroup, Regular semigroup, Inverse semigroup, Cancellative semigroup, Group.

References

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Citation :

Osman Hysa, Orgest Beqiri, "Some Conditions that Turn a Certain Semigroup into a Group," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 3, pp. 54-56, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I3P105