One-sided $S$-systems of operations and character-free proof of Frobenius theorem

TL;DR

This paper presents a new, character-free proof of Frobenius theorem utilizing concepts from ternary operations, orthogonal binary operations, transversals, quasigroups, and loops, offering a novel algebraic perspective.

Contribution

It introduces a character-free proof of Frobenius theorem based on advanced algebraic structures, expanding the theoretical understanding of the theorem.

Findings

Provides a character-free proof of Frobenius theorem

Utilizes concepts from ternary and binary operations

Connects group transversals and quasigroup theories

Abstract

In this work, the author gives a character-free proof of the Frobenius theorem. The new proof is based on some notions and results from the theory of ternary operations, the theory of orthogonal binary operations, the theory of transversals in groups and the theory of quasigroups and loops.