Sandwich Structures from Arbitrary Functions in Group Theory

TL;DR

This paper introduces the concept of sandwiches, a generalization of groups based on sandwich morphisms, and explores their properties and relationship to traditional group structures.

Contribution

It defines sandwich structures as a new algebraic framework and investigates their connection to existing group theory concepts.

Findings

Sandwich structures are left distributive, idempotent, left involutary magmas.

Sandwich morphisms preserve the sandwich structure within groups.

The paper establishes foundational properties linking sandwiches to groups.

Abstract

Functions between groups with the property that all function con- jugates are inverse preserving are called sandwich morphisms. These maps pre- serve a structure within the group known as the sandwich structure. Sandwich structures are left distributive idempotent left involutary magmas. These pro- vide a generalisation of groups which we call a sandwich. This paper explores sandwiches and their relationship to groups.