Classification of subgroups isomorphic to PSL_2(27) in the Monster

TL;DR

This paper proves that the Monster group does not contain any subgroup isomorphic to PSL_2(27), clarifying the subgroup structure of this large sporadic group.

Contribution

The paper establishes a non-existence result for a specific subgroup within the Monster, advancing understanding of its subgroup classification.

Findings

No subgroup isomorphic to PSL_2(27) exists in the Monster

The result refines the subgroup structure knowledge of the Monster

Provides methods potentially applicable to other subgroup classifications

Abstract

We prove that the Monster does not contain any subgroup isomorphic to PSL_2(27).