Some Conditions that Turn a Certain Semigroup into a Group
Osman Hysa, Orgest Beqiri · International Journal of Mathematics Trends and Technology · 2025
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.