Characterization of finite groups with injective maps
Source:
December 16, 2019
group theory
Problem Statement
Let be a finite [url=https://en.wikipedia.org/wiki/Cancellation_property]cancellative semigroup.a) Prove that contains an idempotent element.
b) Prove that is a group.
c) Disprove subpoint b) in the case that would not be finite.
Vlad Mihaly