Search results for "Inner automorphism"

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.

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

Symplectic automorphisms of prime order on K3 surfaces

2006

The aim of this paper is to study algebraic K3 surfaces (defined over the complex number field) with a symplectic automorphism of prime order. In particular we consider the action of the automorphism on the second cohomology with integer coefficients. We determine the invariant sublattice and its perpendicular complement, and show that the latter coincides with the Coxeter-Todd lattice in the case of automorphism of order three. We also compute many explicit examples, with particular attention to elliptic fibrations.

Fixpunktmengen von halbeinfachen Automorphismen in halbeinfachen Lie-Algebren

1976

Let g be a semisimple Lie algebra over an algebraically closed field of characteristic 0. The set of fixed points of a semisimple inner automorphism of g is a regular reductive subalgebra of maximal rank [1], so it is defined by a subsystem of the root system Φ of g relative to a suitable Cartan subalgebra. The main theorem of the article characterizes the corresponding subsystems of Φ. The second part of the article shows how to compute the fixed point algebras of semisimple outer automorphisms of g. A complete list of all fixed point algebras is then easily obtainable. The results are applied to bounded symmetric domains. References

A Series of Hadamard Designs with Large Automorphism Groups

2000

Abstract Whilst studying a certain symmetric (99, 49, 24)-design acted upon by a Frobenius group of order 21, it became clear that the design would be a member of an infinite series of symmetric (2q2 + 1, q2, (q2 − 1)/2)-designs for odd prime powers q. In this note, we present the definition of the series and give some information about the automorphism groups of its members.

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.