نتایج جستجو برای: w nilpotent group
تعداد نتایج: 1165022 فیلتر نتایج به سال:
For any simply connected, simple complex algebraic group, we define upper/lower half-decorated geometric crystals and show that their tropicalization will be normal Kashiwara's crystals. In particular, the of crystal on big Bruhat cell $$ \left(=B{\overline{w}}_0:= {B}^{-}\cap U{\overline{w}}_0U\right) is isomorphic to Langlands dual B(∞) nilpotent-half subalgebra quantum group. As an applicati...
suppose that $h$ is a subgroup of $g$, then $h$ is said to be $s$-permutable in $g$, if $h$ permutes with every sylow subgroup of $g$. if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|, |h|)=1$), then $h$ is called an $s$-semipermutable subgroup of $g$. in this paper, we say that $h$ is partially $s$-embedded in $g$ if $g$ has a normal subgroup $t$ such that $ht...
let $g={rm sl}_2(p^f)$ be a special linear group and $p$ be a sylow $2$-subgroup of $g$, where $p$ is a prime and $f$ is a positive integer such that $p^f>3$. by $n_g(p)$ we denote the normalizer of $p$ in $g$. in this paper, we show that $n_g(p)$ is nilpotent (or $2$-nilpotent, or supersolvable) if and only if $p^{2f}equiv 1,({rm mod},16)$.
we call $h$ an $ss$-embedded subgroup of $g$ if there exists a normal subgroup $t$ of $g$ such that $ht$ is subnormal in $g$ and $hcap tleq h_{sg}$, where $h_{sg}$ is the maximal $s$-permutable subgroup of $g$ contained in $h$. in this paper, we investigate the influence of some $ss$-embedded subgroups on the structure of a finite group $g$. some new results were obtained.
Let V be a finite-dimensional vector space, and let G be a subgroup of GL( V). Set D( V) equal to the algebra of differential operators on V with polynomial coefficients and D( V) G equal to the G invariants in D( V). If 9 is a reductive Lie algebra over C then ~ egis a Cartan subgroup of g, and if G is the adjoint group of 9 then W is the Weyl group of (g, ~) , Harish-Chandra introduced an alg...
In this paper, we study the relation between the cohomology of Coxeter groups and their parabolic subgroups of nite order. Let W be a Coxeter group and k a commutative ring with identity. We investigate the natural map : H (W; k) ! lim:inv: H (W F ; k), where W F runs all parabolic subgroups of nite order, and prove that the kernel and the cokernel of consist of nilpotent elements. This general...
chapter one is devotod to collect some notion and background informations, which are needed in the next chapters. it also contains some important statements which will be proved in a more general context later in this thesis. in chapter two, we show that if the marginal factor-group is of order np1...pk,n>1, then we obtain a bound for the order of the verbal subgroup. also a bound for the bear-...
let $g={rm sl}_2(p^f)$ be a special linear group and $p$ be a sylow $2$-subgroup of $g$, where $p$ is a prime and $f$ is a positive integer such that $p^f>3$. by $n_g(p)$ we denote the normalizer of $p$ in $g$. in this paper, we show that $n_g(p)$ is nilpotent (or $2$-nilpotent, or supersolvable) if and only if $p^{2f}equiv 1,({rm mod},16)$.
A ring R is uniquely (nil) clean in case for any $a in R$ there exists a uniquely idempotent $ein R$ such that $a-e$ is invertible (nilpotent). Let $C =(A V W B)$ be the Morita Context ring. We determine conditions under which the rings $A,B$ are uniquely (nil) clean. Moreover we show that the center of a uniquely (nil) clean ring is uniquely (nil) clean.
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