Automorphisms of certain design groups II

Kostia I. Beidar, Wen-Fong Ke, Hubert Kiechle

Research output: Contribution to journalArticle

Abstract

Let Φ be a group acting semiregularly as automorphisms on the group (N, +). This gives rise to a certain 2-design (N, BΦ). The group structure of N is compatible with the geometric structure of this 2-design, and we call (N, BΦ, +) a design group. Extending our previous results, we study the question of when such design groups are isomorphic. Let Ψ be another group acting on N so that (N, BΨ, +) is also a design group. Suppose further that for k = | Φ | we have | N / [N, N] | > 2 k2 - 6 k + 1. We show that (N, BΦ, +) and (N, BΨ, +) are isomorphic if and only if Φ and Ψ are conjugate in the automorphism group of N.

Original languageEnglish
Pages (from-to)672-686
Number of pages15
JournalJournal of Algebra
Volume313
Issue number2
DOIs
Publication statusPublished - 2007 Jul 15

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Automorphisms
Isomorphic
Geometric Structure
Design
Automorphism Group
If and only if

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Beidar, Kostia I. ; Ke, Wen-Fong ; Kiechle, Hubert. / Automorphisms of certain design groups II. In: Journal of Algebra. 2007 ; Vol. 313, No. 2. pp. 672-686.
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Automorphisms of certain design groups II. / Beidar, Kostia I.; Ke, Wen-Fong; Kiechle, Hubert.

In: Journal of Algebra, Vol. 313, No. 2, 15.07.2007, p. 672-686.

Research output: Contribution to journalArticle

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