TY - JOUR

T1 - Automorphisms of certain design groups II

AU - Beidar, Kostia I.

AU - Ke, Wen Fong

AU - Kiechle, Hubert

N1 - Funding Information:
* Corresponding author. E-mail addresses: wfke@mail.ncku.edu.tw (W.-F. Ke), kiechle@math.uni-hamburg.de (H. Kiechle). 1 The author passed away before this paper was complete. 2 Partially supported by National Science Council, ROC. 3 Partially supported by DAAD.

PY - 2007/7/15

Y1 - 2007/7/15

N2 - 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.

AB - 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.

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U2 - 10.1016/j.jalgebra.2006.11.026

DO - 10.1016/j.jalgebra.2006.11.026

M3 - Article

AN - SCOPUS:34248642885

VL - 313

SP - 672

EP - 686

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 2

ER -