Unable to retrieve citations for this document

Retrieving citations for document...

Radha Kessar
November 6, 2008

Unable to retrieve citations for this document

Retrieving citations for document...

Susanne Danz
November 6, 2008

### Abstract

We prove that the vertices of a completely splittable module D for a finite symmetric group over an algebraically closed field of characteristic p > 0 are precisely the defect groups of the block containing D . We also determine the vertices of simple modules for the symmetric groups in characteristic p > 2 which are labelled by two part partitions ( n – m, m ) such that .

Unable to retrieve citations for this document

Retrieving citations for document...

Mark L. Lewis, John K. McVey
November 6, 2008

Unable to retrieve citations for this document

Retrieving citations for document...

Wolfgang Knapp, Peter Schmid
November 6, 2008

### Abstract

We give a new approach to the celebrated theorem of Frobenius (describing the structure of Frobenius groups). We also study the subgroup of a finite transitive permutation group generated by the fixed point free elements (derangements) and its relation to the Frobenius–Wielandt theorem.

Unable to retrieve citations for this document

Retrieving citations for document...

Pavel Shumyatsky, Carmela Sica
November 6, 2008

### Abstract

Let G be a locally finite group admitting a four-group of automorphisms without non-trivial fixed points. It is shown that the derived group G ′ is a product of normal nilpotent subgroups.

Unable to retrieve citations for this document

Retrieving citations for document...

Wenbin Guo, Alexander N. Skiba
November 6, 2008

### Abstract

Let G be a finite group and ℱ a class of finite groups. We say that G is a quasi-ℱ-group if for every ℱ -eccentric chief factor H / K of G and every x ∈ G , x induces an inner automorphism on H / K . In this paper, the general theory of quasi- ℱ -groups is given and some of its applications are considered. In particular, some characterizations of quasisoluble groups and quasisupersoluble groups are obtained.

Unable to retrieve citations for this document

Retrieving citations for document...

Ágota Figula
November 18, 2008

### Abstract

If the multiplication group Mult( L ) of a connected simply connected 2-dimensional topological loop L is a Lie group, then Mult( L ) is an elementary filiform Lie group ℱ of dimension n + 2 for some n ⩾ 2, and any such group is the multiplication group of a connected simply connected 2-dimensional topological loop L . Moreover, if the group topologically generated by the left translations of L has dimension 3, then L is uniquely determined by a real polynomial of degree n .

Unable to retrieve citations for this document

Retrieving citations for document...

Jang Hyun Jo
November 6, 2008

### Abstract

In 1992, Goichot introduced a complete homology theory for arbitrary groups developed by Vogel. In 1998, Triulzi investigated another complete homology theory using the satellite approach invented by Mislin. These developments provide the motivation to find a new invariant ichd G of a group G , which is related to complete homology theories. We investigate its properties and related questions. In particular, using this invariant, we show that Triulzi complete homology is isomorphic to Vogel–Goichot complete homology in many classes of groups. Also we show that hd G = 0 if and only if G is locally finite when G satisfies one of a number of conditions.

Unable to retrieve citations for this document

Retrieving citations for document...

Michael L. Mihalik, John G. Ratcliffe
November 6, 2008

### Abstract

In this paper, the set of all possible ranks of an arbitrary Coxeter group is determined.

Unable to retrieve citations for this document

Retrieving citations for document...

Stephen P. Humphries
November 6, 2008

### Abstract

For a free group F n = 〈 x 1 , . . . , x n 〉 we investigate when a finite index subgroup of F n is generated by a set 𝒳 of powers of conjugates of the generators x 1 , . . . , x n . For the braid group B n = 〈σ 1 , . . . , σ n –1 〉 we similarly consider when a finite index subgroup is generated by a set of powers of Dehn twists, i.e., conjugates of the elements . We indicate a connection of these problems with the theory of c -groups developed by Burnside, Schur and Wielandt.

Unable to retrieve citations for this document

Retrieving citations for document...

A. O. Asar
November 6, 2008