Abstract
We use the primitive action of the Mathieu group M-22 of degree 672 to define a free product of 672 copies of the cyclic group Z(2) extended by M-22 to form a semidirect product which we denote by P = 2(*672) : M-22. Such a semidirect product is called a progenitor. By investigating a subprogenitor of shape 2(*42) : A(7) we are led to a short relation by which to factor P. We verify that the resulting factor group is McL : 2, the automorphism group of the McLaughlin simple group, and identify it with the familiar permutation group of degree 275.
Original language | English |
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Journal | Communications in Algebra |
DOIs | |
Publication status | Published - 1 Jan 2008 |
Keywords
- McLaughlin
- Symmetric generation
- Sporadic group