Search results for "Combinatorics"

Permutation properties and the fibonacci semigroup

1989

Products of locally dihedral subgroups

2012

AbstractIt is shown that a group G=AB which is a product of two periodic locally dihedral subgroups A and B is soluble.

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.

KNOTS WITH UNKNOTTING NUMBER ONE AND GENERALISED CASSON INVARIANT

1996

We extend the classical notion of unknotting operation to include operations on rational tangles. We recall the “classical” conditions (on the signature, linking form etc.) for a knot to have integral (respectively rational) unknotting number one. We show that the generalised Casson invariant of the twofold branched cover of the knot gives a further necessary condition. We apply these results to some Montesinos knots and to knots with less than nine crossings.

Extending the star order to Rickart rings

2015

Star partial order was initially introduced for semigroups and rings with (proper) involution. In particular, this order has recently been studied on Rickart *-rings. It is known that the star order in such rings can be characterized by conditions not involving involution explicitly. Owing to these characterizations, the order can be extended to certain special Rickart rings named strong in the paper; this extension is the objective of the paper. The corresponding order structure of strong Rickart rings is studied more thoroughly. In particular, the most significant lattice properties of star-ordered Rickart *-rings are successfully transferred to strong Rickart rings; also several new resu…

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

Fitting classes and products of totally permutable groups

2002

The second and third authors have been supported by Proyecto PB 97-0674-C02-02 of DGESIC, Ministerio de Educación y Cultura, Spain.

Zeros of Primitive Characters in Solvable Groups

1999

Subdirectly irreducible generalized sums of upper semilattice ordered systems of algebras

2002

In [15] the generalized sum of an upper (F 1 , F 2 )-semilattice ordered system of algebras was defined. In this paper we find necessary and sufficient conditions under which this construction yields subdirectly irreducible algebras.

Groups whose subgroups satisfy the weak subnormalizer condition

2019

A subgroup X of a group G is said to satisfy the weak subnormalizer condition if $$N_G(Y)\le N_G(X)$$ for each non-normal subgroup Y of G such that $$X\le Y\le N_G(X)$$ . The behaviour of generalized soluble groups whose (cyclic) subgroups satisfy the weak subnormalizer condition is investigated.