๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Loops with Transitive Automorphisms

โœ Scribed by Arthur A. Drisko


Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
199 KB
Volume
184
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

โœฆ Synopsis


It is shown that isotopic loops with transitive automorphism groups are in fact isomorphic. A classification of loops with transitive automorphism groups is given.

ลฝ . This classification is compared to one given by Barlotti and Strambach 1983 for loops with sharply transitive automorphism groups, and examples of several of the classes are presented. The approach is entirely algebraic.


๐Ÿ“œ SIMILAR VOLUMES


Loops of Orderpn+1 with Transitive Autom
โœ Arthur A. Drisko ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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

SGDs with doubly transitive automorphism
โœ Cameron, Peter J. ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 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

On bounded automorphisms of locally fini
โœ Niemeyer, Peter ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 517 KB

The automorphism-group of an infinite graph acts in a natural way on the set of d-fibers (components of the set of rays with respect to the Hausdorff metric). For connected, locally finite, almost transitive graphs the kernel of this action is proved to be the group of bounded automorphisms. This co

Permutation Groups, Vertex-transitive Di
โœ D. Maru sฬ†cฬ†; R. Scapellato ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 120 KB

A nonidentity element of a permutation group is said to be semiregular if all of its orbits have the same length. The work in this paper is linked to [6] where the problem of existence of semiregular automorphisms in vertex-transitive digraphs was posed. It was observed there that every vertextransi

A ๏ฟฝ-transitive graph of valency 4 with a
โœ Maru?i?, Dragan; Xu, Ming-Yao ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 108 KB ๐Ÿ‘ 2 views

A graph X is said to be 1 2 -transitive if its automorphism group acts transitively on the sets of its vertices and edges but intransitively on the set of its arcs. A construction of a 1 2 -transitive graph of valency 4 and girth 6 with a nonsolvable group of automorphism is given.

On Finite Linear Spaces with Almost Simp
โœ Jan Saxl ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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].