# Embedding in a finite 2-generator semigroup

## TL;DR

This paper extends existing results by demonstrating how certain finite semigroups, including those with idempotents forming a band and orthodox semigroups, can be embedded into 2-generator finite semigroups of the same type.

## Contribution

It introduces a method for embedding specific classes of finite semigroups into 2-generator finite semigroups, broadening the understanding of their structural properties.

## Key findings

- Finite semigroups with idempotents forming a band can be embedded into 2-generator semigroups.
- Orthodox semigroups can also be embedded into 2-generator finite semigroups.
- The approach applies to semigroups of the same type, preserving their structural features.

## Abstract

We augment the body of existing results on embedding finite semigroups of a certain type into 2-generator finite semigroups of the same type. The approach adopted applies to finite semigroups the idempotents of which form a band and also to finite orthodox semigroups.