Efficient presentations for the Mathieu simple group M22 and its cover

Simultaneous Constructions of the Sporadic Groups

In this article we give self-contained existence proofs for the sporadic simple groups Co2 and Fi22 using the second author’s algorithm [10] constructing finite simple groups from irreducible subgroups of GLn(2). These two sporadic groups were originally discovered by J. Conway [4] and B. Fischer [7], respectively, by means of completely different and unrelated methods. In this article n = 10 a...

Torsion Units in Integral Group Ring of the Mathieu Simple Group M22

We investigate the possible character values of torsion units of the normalized unit group of the integral group ring of Mathieu sporadic groupM22. We confirm the Kimmerle conjecture on prime graphs for this group andspecify the partial augmentations for possible counterexamples to the stronger Zassenhaus conjecture.

Construction of the Fourfold Cover of the Mathieu Group M22

Torsion Units in Integral Group Ring of the Mathieu Simple Group

We investigate the possible character values of torsion units of thenormalized unit group of the integral group ring of Mathieu sporadic groupM22. We confirm the Kimmerle conjecture on prime graphs for this group andspecify the partial augmentations for possible counterexamples to the strongerZassenhaus conjecture.

The Mathieu groups and designs

In the early 80-ties it became clear that the classification of the non-abelian finite simple groups was complete. Among the finite simple groups we find several families: the alternating groups and various families of groups of Lietype and their twisted analogues. Besides these families there exist 26 sporadic finite simple groups. In these notes we consider five sporadic simple groups, the Ma...