Search results for "Automorphism group"

Some new Hadamard designs with 79 points admitting automorphisms of order 13 and 19

2001

Abstract We have proved that there exists at least 2091 mutually nonisomorphic symmetric (79,39,19)-designs. In particular, 1896 of them admit an action of the nonabelian group of order 57, and an additional 194 an action of the nonabelian group of order 39.

A Classification of all Symmetric Block Designs of Order Nine with an Automorphism of Order Six

2006

We complete the classification of all symmetric designs of order nine admitting an automorphism of order six. As a matter of fact, the classification for the parameters (35,17,8), (56,11,2), and (91,10,1) had already been done, and in this paper we present the results for the parameters (36,15,6), (40,13,4), and (45,12,3). We also provide information about the order and the structure of the full automorphism groups of the constructed designs. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 301–312, 2006

Characterization of strong chain geometries by their automorphism group

1992

A wide class of chain geometries is characterized by their automorphism group using properties of a distinguished involution.

Some Hadamard designs with parameters (71,35,17)

2002

Up to isomorphisms there are precisely eight symmetric designs with parameters (71, 35, 17) admitting a faithful action of a Frobenius group of order 21 in such a way that an element of order 3 fixes precisely 11 points. Five of these designs have 84 and three have 420 as the order of the full automorphism group G. If |G| = 420, then the structure of G is unique and we have G = (Frob21 × Z5):Z4. In this case Z(G) = 〈1〉, G′ has order 35, and G induces an automorphism group of order 6 of Z7. If |G| = 84, then Z(G) is of order 2, and in precisely one case a Sylow 2-subgroup is elementary abelian. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 144–149, 2002; DOI 10.1002/jcd.996

Injective Fitting sets in automorphism groups

1993

Automorphisms of the integral group ring of the hyperoctahedral group

1990

The purpose of this paper is to verify a conjecture of Zassenhaus [3] for hyperoctahedral groups by proving that every normalized automorphism () of ZG can be written in the form () = Tu 0 I where I is an automorphism of ZG obtained by extending an automorphism of G linearly to ZG and u is a unit of (JJG. A similar result was proved for symmetric groups by Peterson in [2]; the reader should consult [3] or the survey [4] for other results of this kind. 1989

Symmetric (79, 27, 9)-designs Admitting a Faithful Action of a Frobenius Group of Order 39

1997

AbstractIn this paper we present the classification of symmetric designs with parameters (79, 27, 9) on which a non-abelian group of order 39 acts faithfully. In particular, we show that such a group acts semi-standardly with 7 orbits. Using the method of tactical decompositions, we are able to construct exactly 1320 non-isomorphic designs. The orders of the full automorphism groups of these designs all divide 8 · 3 · 13.

Quotients of the Dwork Pencil

2012

In this paper we investigate the geometry of the Dwork pencil in any dimension. More specifically, we study the automorphism group G of the generic fiber of the pencil over the complex projective line, and the quotients of it by various subgroups of G. In particular, we compute the Hodge numbers of these quotients via orbifold cohomology.

On permutations of class sums of alternating groups

1997

We prove a result concerning the class sums of the alternating group An; as a consequence we deduce that if θ is a normalized automorphism of the integral group ring then there exists such that is the identity on , where Sn:is the symmetric group and is the center of

Automorphisms of 2–dimensional right-angled Artin groups

2007

We study the outer automorphism group of a right-angled Artin group AA in the case where the defining graph A is connected and triangle-free. We give an algebraic description of Out.AA/ in terms of maximal join subgraphs in A and prove that the Tits’ alternative holds for Out.AA/. We construct an analogue of outer space for Out.AA/ and prove that it is finite dimensional, contractible, and has a proper action of Out.AA/. We show that Out.AA/ has finite virtual cohomological dimension, give upper and lower bounds on this dimension and construct a spine for outer space realizing the most general upper bound. 20F36; 20F65, 20F28