Probabilistic generation of finite classical groups in odd characteristic by involutions
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Abstract
An involution in a finite n-dimensional classical group G over a field of odd order q is called (α, β)-balanced if the dimension of its fixed point subspace is between αn and βn. Balanced involutions play an important role in recent constructive recognition algorithms for finite classical groups in odd characteristic. For a given sequence 
of conjugacy classes of balanced involutions in G, a c-tuple (g1, . . . , gc) is a class-random sequence from 𝒳 if, for each i = 1, . . . , c, gi is a uniformly distributed random element of 
, and the gi are mutually independent. We show that there is a number c = c(α, β) such that for large enough n, for a given such sequence 𝒳 of length c, a class-random sequence from 𝒳 generates a subgroup containing the generalized Fitting subgroup of G with probability at least 1 – q–n.
© de Gruyter 2011
Articles in the same Issue
- Spinal groups: semidirect product decompositions and Hausdorff dimension
- Probabilistic generation of finite classical groups in odd characteristic by involutions
- Small loops of nilpotency class 3 with commutative inner mapping groups
- Persistent homology of groups
- Right orderability and graphs of groups
- Steinberg lattice of the general linear group and its modular reduction
- Maximal representation dimension of finite p-groups
Articles in the same Issue
- Spinal groups: semidirect product decompositions and Hausdorff dimension
- Probabilistic generation of finite classical groups in odd characteristic by involutions
- Small loops of nilpotency class 3 with commutative inner mapping groups
- Persistent homology of groups
- Right orderability and graphs of groups
- Steinberg lattice of the general linear group and its modular reduction
- Maximal representation dimension of finite p-groups
