P. G. Morje, A nearly linear time algorithm for Sylow subgroups of permutation groups. Ph.D. thesis, Ohio State U. 1995.  Home/Search   Document Not in Database   Summary   Related Articles

.... deterministic polynomial time [FHL;Lu2] Monte Carlo polynomial time [CF] and parallel (complexity class NC) LM;Lu1;Lu3;KLM] However, no procedure is known for (B5) in the context of nearly linear time computation, so that only a few of our results apply to that model of computation (cf. [Mo]) In addition to (B1 5) we presuppose various other simple procedures, such as working with subsets of our permutation domain and factoring the order of a group into primes. In Section 6 we will prove our main result: Theorem 2.3. There is an algorithm NATURAL ACTION using only procedures for ....

....a group G of linear transformations whose quotient, modulo scalars, is G and such that the group of permutations induced by G on the set of all 1 spaces of V is permutation isomorphic to that of G on the set Pi constructed in NATURAL ACTION. All of this can be found in [Ka3] Ma] and [Mo] in the sequential, parallel and nearly linear settings, respectively. The approach is fairly simple, and will undoubtedly also work well in practical contexts. There does not seem to be any point in reproducing those algorithms here, so we will simply outline what is involved, frequently using ....

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P. G. Morje, A nearly linear time algorithm for Sylow subgroups of permutation groups. Ph.D. thesis, Ohio State U. 1995.

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