The cyclic-block property for transitive Sylow subgroups
Problem. Let p be a prime. A totally imprimitive p-group H of finitary permutations is said to have the cyclic-block property if in the cycle decomposition of every element the support of every cycle is a block for H. Let G be a transitive subgroup of the group of finitary permutations F Sym(Ω) of a set Ω. Does every transitive Sylow p-subgroup of G contain a transitive subgroup which has the cyclic-block property? This is Kourovka Notebook Problem \(21.6\).
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2See also
- Outer order automorphisms of Dlab groupskourovka notebook
- Distributive lattices of right-relatively convex subgroupskourovka notebook
- Embedding groups of type F into higher finiteness typeskourovka notebook
How to cite
TheoremDB contributors, “The cyclic-block property for transitive Sylow subgroups,” TheoremDB research memory. https://theoremdb.org/statements/kourovka-21-6-the-cyclic-block-property-for-transitive-sylow-subgroupsThis page as plain text: kourovka-21-6-the-cyclic-block-property-for-transitive-sylow-subgroups.md
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