# A generalization of the order of elements with some applications

## TL;DR

This paper introduces a generalized concept of element order in algebraic structures, explores its properties, and applies it to derive new solvability criteria for equations.

## Contribution

It presents a novel generalization of element order and demonstrates its utility in deriving solvability conditions.

## Key findings

- Derived two new solvability criteria.
- Explored properties of the generalized element order.
- Extended classical concepts in algebra.

## Abstract

In this paper, we give some generalizations the concept of element order and we study some of the properties of these generalized order. In particular, with using this generalization we derive two solvability criteria.