### Abstract

Let Φ be a group acting semiregularly as automorphisms on the group (N, +). This gives rise to a certain 2-design (N, B_{Φ}). The group structure of N is compatible with the geometric structure of this 2-design, and we call (N, B_{Φ}, +) 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, B_{Ψ}, +) is also a design group. Suppose further that for k = | Φ | we have | N / [N, N] | > 2 k^{2} - 6 k + 1. We show that (N, B_{Φ}, +) and (N, B_{Ψ}, +) are isomorphic if and only if Φ and Ψ are conjugate in the automorphism group of N.

Original language | English |
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Pages (from-to) | 672-686 |

Number of pages | 15 |

Journal | Journal of Algebra |

Volume | 313 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2007 Jul 15 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Journal of Algebra*,

*313*(2), 672-686. https://doi.org/10.1016/j.jalgebra.2006.11.026

}

*Journal of Algebra*, vol. 313, no. 2, pp. 672-686. https://doi.org/10.1016/j.jalgebra.2006.11.026

**Automorphisms of certain design groups II.** / Beidar, Kostia I.; Ke, Wen-Fong; Kiechle, Hubert.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Automorphisms of certain design groups II

AU - Beidar, Kostia I.

AU - Ke, Wen-Fong

AU - Kiechle, Hubert

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.

UR - http://www.scopus.com/inward/record.url?scp=34248642885&partnerID=8YFLogxK

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U2 - 10.1016/j.jalgebra.2006.11.026

DO - 10.1016/j.jalgebra.2006.11.026

M3 - Article

VL - 313

SP - 672

EP - 686

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 2

ER -