Automorphisms of certain design groups II

Kostia I. Beidar, Wen Fong Ke, Hubert Kiechle

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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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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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