THEOREM. Let G be a finite group and s an involution in G, such that CG(S)~CGQ(SO)Assume G^Co(s)0(G) (0(G) is the maximal normal odd order subgroup of G). Then Gc^Go. In particular, G has the following properties : (i) G has order 2 • 3 • 5 • 7 • 11 • 23, and is simple. (ii) G has two conjugacy classes of involutions. One class is represented by the involution s. A representative t of the secon...

this article presents a unified approach to the abstract notions of partial convolution and involution in $l^p$-function spaces over semi-direct product of locally compact groups. let $h$ and $k$ be locally compact groups and $tau:hto aut(k)$ be a continuous homomorphism.  let $g_tau=hltimes_tau k$ be the semi-direct product of $h$ and $k$ with respect to $tau$. we define left and right $tau$-c...

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...

We construct an infinite family of topologically slice knots that are not smoothly concordant to their reverses. More precisely, if $$\mathcal {T}$$ denotes the concordance group and $$\rho $$ is involution induced by string reversal, then {T}/ \text {Fix}(\rho )$$ contains infinitely generated free subgroup. The result remains true modulo subgroup with trivial Alexander polynomial.

We present a number of new characterizations of EP elements in rings with involution in purely algebraic terms. Then, we study equivalent conditions for an element a in a ring with involution to satisfy ana∗ = a∗an or a = (a∗)n for arbitrary n ∈ N . For n = 1, we present some new characterizations of normal and Hermitian elements in rings with involution.

Let $FG$ be the group algebra of a finite $p$-group $G$ over a
 field $F$ characteristic $p$ and let $*$ the
 classical involution $FG$. The $*$-unitary subgroup $FG$,
 denoted by $V_*(FG)$, is defined to set all normalized
 units $u$ satisfying property $u^*=u^{-1}$. In this paper we
 give recursive method how compute order for certain non-commutative algebras.
 A...

A ring R is called clean if every element of the sum a unit and an idempotent. Motivated by question proposed Lam on cleanness von Neumann Algebras, Vaš introduced more natural concept for ?-rings, ?-cleanness. More precisely, ?-ring ?- projection (?-invariant idempotent). Let F be finite field G abelian group. In this paper, we introduce two classes involutions group rings form characterize ?-...

We provide a simple criterion for an element of the mapping class group closed surface to be normal generator group. apply this show that every nontrivial periodic is not hyperelliptic involution when genus at least 3. also give many examples pseudo-Anosov generators, answering question D. Long. In fact we with stretch factor less than $\\sqrt{2}$ generator. Even more, generators arbitrarily la...

Abstract We prove that real topological Hochschild homology $\mathrm {THR}$ for schemes with involution satisfies base change and descent the ${\mathbb {Z}/2}$ -isovariant étale topology. As an application, we provide computations projective line (with without involution) higher-dimensional spaces.