On the Mathieu groups M22 and M11

Construction of the Fourfold Cover of the Mathieu Group M22

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...

Mathieu Groups

In this essay, we will discuss some interesting properties of the Mathieu groups, which are a family of five sporadic finite simple groups, as well as some closely related topics. One construction of the Mathieu groups involves Steiner systems, so we will begin by discussing Steiner systems.

Efficient presentations for the Mathieu simple group M22 and its cover

Questions about the efficiency of finite simple groups and their covering groups have been the subject of much research. We provide new efficient presentations for the Mathieu simple group M22 and its cover, including the shortest known efficient presentation for M22 and a somewhat longer presentation which is very suitable for computation. 2000 Mathematics Subject Classification: 20-04, 20D05,...

Clifford quantum computer and the Mathieu groups

One learned from Gottesman-Knill theorem that the Clifford model of quantum computing [11] may be generated from a few quantum gates, the Hadamard, π/4-Phase and Controlled-Z gates, and efficiently simulated on a classical computer. We employ the group theoretical package GAP[10] for simulating the two qubit Clifford group C2. We already found that the symmetric group S(6), aka the automorphism...