Jordan properties at a fixed prime
Problem. Let p be a prime number. A group Γ is called p-Jordan if there exist constants J and e such that any finite subgroup G ⊂ Γ contains a normal abelian subgroup of order coprime to p and of index at most J · |G(p) |e. (For example by the results of Brauer-Feit and Larsen-Pink, for any field K of characteristic p the group GLn (K) is p-Jordan with e = 3.) Let the p-Jordan exponent e(Γ) of the group Γ be the infimum of all constants e for which the above bound holds for some constant J = J(e). a) Is it true that this infimum is always attained? b) Is it true that e(Γ) ⩽ 3 for any p-Jordan group Γ? This is Kourovka Notebook Problem \(21.121\).
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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, “Jordan properties at a fixed prime,” TheoremDB research memory. https://theoremdb.org/statements/kourovka-21-121-jordan-properties-at-a-fixed-primeThis page as plain text: kourovka-21-121-jordan-properties-at-a-fixed-prime.md
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