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Solution to Dempwolff’s nonsolvable B-group problem. (English) Zbl 0612.51002

Given a translation plane of even order \(q^ 2=2^ n\geq 16\). Let \(\pi\) be the corresponding spread, and G be a subgroup of \(Aut \pi\). A subgroup S of G is called a B-group if S is a 2-group of order greater than \(\sqrt{q}\) and Fix(S) is a Baer subplane of the translation plane. Let G* be the group generated by the union of all B-groups in G having maximum cardinality. - Theorem. (a) If G* is nonsolvable then \(\pi\) is a Hall plane or a known plane of order 16. (b) If G* is solvable and G contains a B-group of order \(\neq \sqrt{2q}\) (e.g. when q is a square) then G* is an elementary abelian B-group.
Reviewer: F.Knüppel

MSC:

51A40 Translation planes and spreads in linear incidence geometry
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
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References:

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