On invariable generation of alternating groups by elements of prime and prime power order

TL;DR

This paper proves that all alternating groups up to degree one quadrillion can be generated invariable by a prime order element and a prime power order element, extending understanding of their generative properties.

Contribution

It establishes a universal invariable generation property for alternating groups of extremely large degree, specifically by elements of prime and prime power order.

Findings

Every alternating group up to degree one quadrillion is invariable generated by specified elements.

The result confirms a broad generative property for large alternating groups.

Supports the conjecture on invariable generation in finite simple groups.

Abstract

We verify that every alternating group of degree at most one quadrillion is invariably generated by an element of prime order together with an element of prime power order.