✦ LIBER ✦

SGDs with doubly transitive automorphism group

✍ Scribed by Cameron, Peter J.

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 168 KB
Volume: 32
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199911)32:3<229::aid-jgt2>3.0.co;2-c

No coin nor oath required. For personal study only.

✦ Synopsis

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 the determination can be completed, such as those that admit a 3-transitive group, and those with λ = 1. The latter case includes the determination of all near 1factorizations of K n (partitions of the edge set into subsets each of which consists of disjoint edges covering all but one point), which admit 2-transitive groups.

📜 SIMILAR VOLUMES

Constructing 4-Valent 12-Transitive Grap

Constructing 4-Valent 12-Transitive Graphs with a Nonsolvable Automorphism Group

✍ Aleksander Malnič; Dragan Marušič 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 149 KB

A graph is said to be 1 2 -transitive if its automorphism group acts transitively on vertices and edges but not on arcs. For each n 11, a 1 2 -transitive graph of valency 4 and girth 6, with the automorphism group isomorphic to A n \_Z 2 , is given.

Loops of Orderpn+1 with Transitive Autom

Loops of Orderpn+1 with Transitive Automorphism Groups

✍ Arthur A. Drisko 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 239 KB

It is shown that isotopic loops of order p n +1, p a prime, which have transitive automorphism groups are in fact isomorphic. The proof uses the Sylow theorems to obtain an isomorphism from an arbitrary isotopism. The result is applied to the additive loops of neofields of order p n +1. ## 1997 Aca

Loops with Transitive Automorphisms

✍ Arthur A. Drisko 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 199 KB

It is shown that isotopic loops with transitive automorphism groups are in fact isomorphic. A classification of loops with transitive automorphism groups is given. Ž . This classification is compared to one given by Barlotti and Strambach 1983 for loops with sharply transitive automorphism groups,

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 __

Groups with Anomalous Automorphisms

✍ Rolf Brandl; Libero Verardi 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 172 KB

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.

On Finite Linear Spaces with Almost Simp

On Finite Linear Spaces with Almost Simple Flag-Transitive Automorphism Groups

✍ Jan Saxl 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 280 KB

This paper contains a classification of finite linear spaces with an automorphism group which is an almost simple group of Lie type acting flag-transitively. This completes the proof of the classification of finite flag-transitive linear spaces announced in [BDDKLS].