Unable to retrieve citations for this document

Retrieving citations for document...

T. De Medts, F. Haot, K. Tent, H. Van Maldeghem
July 27, 2005

### Abstract

Let ( G, B, N ) be a group with an irreducible spherical BN-pair of rank at least 2, and let U be a nilpotent normal subgroup of B such that B = U ( B ⋂ N ). We show that U is unique with respect to B . As a corollary, we obtain a complete classification of all irreducible spherical split BN-pairs of rank at least two.

Unable to retrieve citations for this document

Retrieving citations for document...

Fernando Szechtman
July 27, 2005

### Abstract

We show that, in characteristic 2, the Steinberg representation of the symplectic group Sp 2n ( q ), for q a power of an odd prime p , has two irreducible constituents, lying just above the socle, which are isomorphic to the two Weil modules of degree .

Unable to retrieve citations for this document

Retrieving citations for document...

Anna A. Osinovskaya
July 27, 2005

### Abstract

Restrictions of irreducible p -restricted representations of algebraic groups of type A n to naturally embedded subgroups of type A 2 are studied. Let n > 2 and ω = Σ n i=1 m i ω i be the highest weight of the representation considered. The composition factors of such restrictions are determined in the cases where either n > 5 and Σ n i=1 m i < p , or n > 3 and m i + m i +1 + m i +2 + m i +3 < p − 2 for odd i with 1 ≤ i ≤ and m n−j− 3 + m n−j− 2 + m n−j− 1 + m n−j < p − 2 for even j with 0 ≤ j ≤ . For arbitrary p -restricted representations some large composition factors are found.

Unable to retrieve citations for this document

Retrieving citations for document...

Leonid A. Kurdachenko, Javier Otal
July 27, 2005

### Abstract

A theorem of B. H. Neumann shows that groups in which every subgroup has finitely many conjugates are central-by-finite. In this paper, we study groups G such that G /Core G ( N G ( H )) is Chernikov for every subgroup H of G . We show that they are abelian-by-Chernikov and that their derived subgroups are Chernikov, but that they are not necessarily central-by-Chernikov.

Unable to retrieve citations for this document

Retrieving citations for document...

Özgün Ünlü
July 27, 2005

### Abstract

We give counter-examples to [5, Conjecture 1.1]. Example 1 is a 2-group G of order 128 for which axe( G ) = 3 and saw( G ) = 4. In Example 2, for p, q prime numbers with q ≡ 1 mod p , we give a supersolvable group G pq of order p 2 q p+1 with axe( G pq ) = p + 1 and saw( G pq = p + 2. Our smallest example has of order 108 = 2 2 3 2+1 and all of our examples are minimal in the sense that they have no proper subgroup with unequal axe and saw rank.

Unable to retrieve citations for this document

Retrieving citations for document...

Karl H. Hofmann, Sidney A. Morris
July 27, 2005

Cite
Requires Authentication
Accessible
PDF
Unable to retrieve citations for this document

Retrieving citations for document...

S. V. Ivanov
July 27, 2005

### Abstract

Let U be an arbitrary word in letters x ±1 1 , …, x ±1 m and m ≥ 2. We prove that the group presentation 〈 x 1 , …, x m ∥ Ux i U −1 = x i+1 , i = 1, …, m − 1〉 is aspherical. The proof is based upon prior partial results of A. Klyachko and the author on the asphericity of such presentations.