Search results for "Outer automorphism group"

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

Automorphisms of hyperelliptic GAG-codes

2009

Abstract We determine the n –automorphism group of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic function fields. Such group is, up to isomorphism, a subgroup of the automorphism group of the underlying function field.

On the automorphism group of the integral group ring of Sk wr Sn

1992

Abstract Let G = SkwrSn be the wreath product of two symmetric groups Sk and Sn. We prove that every normalized automorphism θ of the integral group ring Z G can be written in the form θ = γ ° τu, where γ is an automorphism of G and τu denotes the inner automorphism induced by a unit u in Q G.

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

Characterization of chain geometries of finite dimension by their automorphism group

1990

A large class of chain geometries of finite dimension is characterized as strong chain spaces possessing a distinguished group of automorphisms fixing two distant points.

Divisible Designs Admitting, as an Automorphism Group, an Orthogonal Group or a Unitary Group

2001

We construct some divisible designs starting from a projective space. These divisible designs admit an orthogonal group or a unitary group as an automorphism group.

Injective Fitting sets in automorphism groups

1993

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

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

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