A 2-Sylow subgroup of J is elementary abelian of order 8 and J has no subgroup of index 2. If r is an involution in J, then C(r) = (r) X K, where K _ A5. Let G be a finite group with the following properties: (a) S2-subgroups of G are abelian; (b) G has no subgroup of index 2; and (c) G contains an involution t such that 0(t) = (t) X F, where F A5. Then G is a (new) simple group isomorphic to J...

Proper selection of material in manufacturing firms is a vital role of designer depending upon the different era of application. The material selection problem is very complex and challenging task today. Erroneous cull of material frequently leads to astronomically immense cost involution, and finally drives towards unfortunate component or product breakdown. Thus, the designer necessitates dis...

In this paper we define a notion of Witt group for sesquilinear forms in hermitian categories, which in turn provides a notion of Witt group for sesquilinear forms over rings with involution. We also study the extension of scalars for K-linear hermitian categories, where K is a field of characteristic 6= 2. We finally extend several results concerning sesquilinear forms to the setting of system...

Morphogenetic cell movements mould the shape of the developing organism. These movements have been extensively studied during Drosophila embryonic development. In particular live imaging analyses have revealed the complexities underlying the comparatively simple processes of germband extension, retraction and dorsal closure. I am applying live imaging techniques to an apparently complex morphog...

Morphogenetic cell movements mould the shape of the developing organism. These movements have been extensively studied during Drosophila embryonic development. In particular live imaging analyses have revealed the complexities underlying the comparatively simple processes of germband extension, retraction and dorsal closure. I am applying live imaging techniques to an apparently complex morphog...

For a black box group G and t an involution of G we describe a computational procedure which produces elements of CG(t) by making use of the local fusion graph F(G, X), where X is the G-conjugacy class of t.

Let G be a simple algebraic group over an algebraically closed field k of bad characteristic. We classify the spherical unipotent conjugacy classes of G. We also show that if the characteristic of k is 2, then the fixed point subgroup of every involutorial automorphism (involution) of G is a spherical subgroup of G.

We introduce and study affine analogues of the fixed-point-free (FPF) involution Stanley symmetric functions Hamaker, Marberg, Pawlowski. Our methods use theory quasiparabolic sets introduced by Rains Vazirani, we prove that subset FPF-involutions is a set for group under conjugation. Using properties sets, transition formula FPF functions, analogous to Lascoux Schützenberger's Schubert polynom...

1. Definition and Examples (p.2) 2. Transvections and Holonomy (p.7) 3. Killing Fields (p.9) 4. Cartan Involution and Cartan Decomposition (p.11) 5. Locally Symmetric Spaces (p.15) 6. Compact, Noncompact and Euclidean Type; Duality (p.16) 7. The Isometry Group (p.17) 8. Lie Subtriples and Totally Geodesic Subspaces (p.19) 9. Isotropy Representation and Rank (p.19) 10. The Weyl Group (p. 22) Ref...

Let $X$ be a finitistic space with the mod $2$ cohomology of product projective and $4$-sphere. Assume that admits free involution. In this paper we study algebra quotient by action involution derive some consequences regarding existence $\mathbb{Z}\_2$-equivariant maps between such an $n$-sphere.