On minimal factorisations of sporadic groups.

Holmes, P.E.

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Displaying similar documents to “On minimal factorisations of sporadic groups.”

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It is a consequence of the classification of finite simple groups that every non-abelian simple group contains a subgroup which is a minimal simple group.

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S. Bezuglyi, K. Medynets (2008)

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We consider the full group [φ] and topological full group [[φ]] of a Cantor minimal system (X,φ). We prove that the commutator subgroups D([φ]) and D([[φ]]) are simple and show that the groups D([φ]) and D([[φ]]) completely determine the class of orbit equivalence and flip conjugacy of φ, respectively. These results improve the classification found in [GPS]. As a corollary of the technique used, we establish the fact that φ can be written as a product of three involutions from [φ]. ...

Two commuting maps without common minimal points

Tomasz Downarowicz (2011)

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We construct an example of two commuting homeomorphisms S, T of a compact metric space X such that the union of all minimal sets for S is disjoint from the union of all minimal sets for T. In other words, there are no common minimal points. This answers negatively a question posed in [C-L]. We remark that Furstenberg proved the existence of "doubly recurrent" points (see [F]). Not only are these points recurrent under both S and T, but they recur along the same sequence of powers. Our...

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Necessary conditions are found for a Cantor subset of the circle to be minimal for some $C^{1}$ -diffeomorphism. These conditions are not satisfied by the usual ternary Cantor set.

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