Symmetric generation of M₂₂

ABSTRACT

We give a computer-free proof that the Mathieu group M₂₂ is a homomorphic image of the progenitor $2^{\star 14}:L_3\left(2\right)$ factorized by three relations.

KEYWORDS:

• Group Theory
• Symmetric Generation
• Sporadic Groups

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 20F05
• Secondary 20D05

Acknowledgment

We thank the referee for his/her invaluable input on an earlier version of this manuscript.

Notes

¹There is a more general notion of progenitor where one replaces C₂ with an arbitrary finite group H, see [10, Section 3] or [11]. We will not need this here.