✦ LIBER ✦

Groups with Anomalous Automorphisms

✍ Scribed by Rolf Brandl; Libero Verardi

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 172 KB
Volume: 183
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0211

No coin nor oath required. For personal study only.

✦ Synopsis

Let Aut G be the group of all automorphisms of a group G that fix all nn Ž . nonnormal subgroups of G. It is shown that Aut G has a very restricted nn structure.

📜 SIMILAR VOLUMES

Automorphisms of Automorphism Groups of

Automorphisms of Automorphism Groups of Free Groups

✍ Martin R. Bridson; Karen Vogtmann 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 87 KB

If n G 3 and F is free of rank n, then Out Aut F s Out Out F s 1 . n n n ᮊ 2000 Academic Press n is an isomorphism. Tits's theorem leads to a proof that the outer automor-

Graphs with symmetric automorphism group

✍ W. D. Wallis; Katherine Heinrich 📂 Article 📅 1978 🏛 John Wiley and Sons 🌐 English ⚖ 333 KB

## Abstract We investigate the properties of graphs whose automorphism group is the symmetric group. In particular, we characterize graphs on less than 2__n__ points with group __S~n~__, and construct all graphs on __n__ + 3 points with group __S~n~__. Graphs with 2__n__ or more points and group __

SGDs with doubly transitive automorphism

SGDs with doubly transitive automorphism group

✍ Cameron, Peter J. 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 168 KB

Symmetric graph designs, or SGDs, were defined by Gronau et al. as a common generalization of symmetric BIBDs and orthogonal double covers. This note gives a classification of SGDs admitting a 2-transitive automorphism group. There are too many for a complete determination, but in some special cases

Groups and Lie Algebras with Almost Regu

Groups and Lie Algebras with Almost Regular Automorphisms

✍ Y.A. Medvedev 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 358 KB

It is proved that if a locally nilpotent group \(G\) admits an almost regular automorphism of prime order \(p\) then \(G\) contains a nilpotent subgroup \(G_{1}\) such that \(\left|G: G_{1}\right| \leqslant f(p, m)\) and the class of nilpotency of \(G_{1} \leqslant g(p)\), where \(f\) is a function

Automorphisms of Certain Design Groups

✍ W.F. Ke; H. Kiechle 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 499 KB

Classification of designs with nontrivia

Classification of designs with nontrivial automorphism groups

✍ Ziba Eslami 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 103 KB

## Abstract In this article, we introduce a new orderly backtrack algorithm with efficient isomorph rejection for classification of __t__‐designs. As an application, we classify all simple 2‐(13,3,2) designs with nontrivial automorphism groups. The total number of such designs amounts to 1,897,386.