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Generating triples of involutions of large sporadic groups
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A. V. Timofeenko
Veröffentlicht/Copyright:
1. Juli 2003
In each finite simple sporadic group, excepting the Baby Monster group B, the Monster group M, the McLaughlin group McL and Mathieu groups M11, M22 , M23, three generating involutions, two of which commute, are found.
If G is one of the groups M12, M24 , HS, J1, J2, J3, then we give pairs of numbers p, q, p ≤ q, such that p = |ik|, q = |jk| for some involutions i , j , k with condition |ij| = 2 generating the group G. The triples of involutions mentioned above are found with the use of the system of computer algebra GAP. Recall that any two involutions of the triple of involutions generating either McL, or M11, or M22, or M23 do not commute.
Published Online: 2003-07-01
Published in Print: 2003-07-01
Copyright 2003, Walter de Gruyter
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Artikel in diesem Heft
- Independent systems of automata in labyrinths
- Estimation of the time needed to set up a covert channel
- Schemes of public distribution of keys based on a non-commutative group
- Characteristic polynomials of multi-index transportation problems
- Construction of maximally non-Hamiltonian graphs
- Generating triples of involutions of large sporadic groups
- On the number of reversible homogeneous structures
- Random partitions of a set with given number of blocks
- On two statistics of chi-square type based on frequencies of tuples of states of a high-order Markov chain
