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Search: All articles in the CMB digital archive with keyword finite group

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1. CMB 2016 (vol 60 pp. 165)

Morimoto, Masaharu
 Cokernels of Homomorphisms from Burnside Rings to Inverse Limits Let $G$ be a finite group and let $A(G)$ denote the Burnside ring of $G$. Then an inverse limit $L(G)$ of the groups $A(H)$ for proper subgroups $H$ of $G$ and a homomorphism ${\operatorname{res}}$ from $A(G)$ to $L(G)$ are obtained in a natural way. Let $Q(G)$ denote the cokernel of ${\operatorname{res}}$. For a prime $p$, let $N(p)$ be the minimal normal subgroup of $G$ such that the order of $G/N(p)$ is a power of $p$, possibly $1$. In this paper we prove that $Q(G)$ is isomorphic to the cartesian product of the groups $Q(G/N(p))$, where $p$ ranges over the primes dividing the order of $G$. Keywords:Burnside ring, inverse limit, finite groupCategories:19A22, 57S17

2. CMB 2016 (vol 59 pp. 392)

Prajapati, S. K.; Sarma, R.
 Total Character of a Group $G$ with $(G,Z(G))$ as a Generalized Camina Pair We investigate whether the total character of a finite group $G$ is a polynomial in a suitable irreducible character of $G$. When $(G,Z(G))$ is a generalized Camina pair, we show that the total character is a polynomial in a faithful irreducible character of $G$ if and only if $Z(G)$ is cyclic. Keywords:finite groups, group characters, total charactersCategory:20C15

3. CMB 2015 (vol 58 pp. 538)

Li, Lili; Chen, Guiyun
 Minimal Non Self Dual Groups A group $G$ is self dual if every subgroup of $G$ is isomorphic to a quotient of $G$ and every quotient of $G$ is isomorphic to a subgroup of $G$. It is minimal non-self dual if every proper subgroup of $G$ is self dual but $G$ is not self dual. In this paper, the structure of minimal non-self dual groups is determined. Keywords:minimal non-self dual group, finite group, metacyclic group, metabelian groupCategory:20D15

4. CMB 2014 (vol 58 pp. 182)

Tărnăuceanu, Marius
 On Finite Groups with Dismantlable Subgroup Lattices In this note we study the finite groups whose subgroup lattices are dismantlable. Keywords:finite groups, subgroup lattices, dismantlable lattices, planar lattices, crownsCategories:20D30, 20D60, 20E15

5. CMB 2014 (vol 57 pp. 884)

Xu, Yong; Zhang, Xinjian
 $m$-embedded Subgroups and $p$-nilpotency of Finite Groups Let $A$ be a subgroup of a finite group $G$ and $\Sigma : G_0\leq G_1\leq\cdots \leq G_n$ some subgroup series of $G$. Suppose that for each pair $(K,H)$ such that $K$ is a maximal subgroup of $H$ and $G_{i-1}\leq K \lt H\leq G_i$, for some $i$, either $A\cap H = A\cap K$ or $AH = AK$. Then $A$ is said to be $\Sigma$-embedded in $G$; $A$ is said to be $m$-embedded in $G$ if $G$ has a subnormal subgroup $T$ and a $\{1\leq G\}$-embedded subgroup $C$ in $G$ such that $G = AT$ and $T\cap A\leq C\leq A$. In this article, some sufficient conditions for a finite group $G$ to be $p$-nilpotent are given whenever all subgroups with order $p^{k}$ of a Sylow $p$-subgroup of $G$ are $m$-embedded for a given positive integer $k$. Keywords:finite group, $p$-nilpotent group, $m$-embedded subgroupCategories:20D10, 20D15

6. CMB 2011 (vol 55 pp. 673)

Aizenbud, Avraham; Gourevitch, Dmitry
 Multiplicity Free Jacquet Modules Let $F$ be a non-Archimedean local field or a finite field. Let $n$ be a natural number and $k$ be $1$ or $2$. Consider $G:=\operatorname{GL}_{n+k}(F)$ and let $M:=\operatorname{GL}_n(F) \times \operatorname{GL}_k(F)\lt G$ be a maximal Levi subgroup. Let $U\lt G$ be the corresponding unipotent subgroup and let $P=MU$ be the corresponding parabolic subgroup. Let $J:=J_M^G: \mathcal{M}(G) \to \mathcal{M}(M)$ be the Jacquet functor, i.e., the functor of coinvariants with respect to $U$. In this paper we prove that $J$ is a multiplicity free functor, i.e., $\dim \operatorname{Hom}_M(J(\pi),\rho)\leq 1$, for any irreducible representations $\pi$ of $G$ and $\rho$ of $M$. We adapt the classical method of Gelfand and Kazhdan, which proves the multiplicity free" property of certain representations to prove the multiplicity free" property of certain functors. At the end we discuss whether other Jacquet functors are multiplicity free. Keywords:multiplicity one, Gelfand pair, invariant distribution, finite groupCategories:20G05, 20C30, 20C33, 46F10, 47A67

7. CMB 2004 (vol 47 pp. 530)

Iranmanesh, A.; Khosravi, B.
 A Characterization of $PSU_{11}(q)$ Order components of a finite simple group were introduced in [4]. It was proved that some non-abelian simple groups are uniquely determined by their order components. As the main result of this paper, we show that groups $PSU_{11}(q)$ are also uniquely determined by their order components. As corollaries of this result, the validity of a conjecture of J. G. Thompson and a conjecture of W. Shi and J. Bi both on $PSU_{11}(q)$ are obtained. Keywords:Prime graph, order component, finite group,simple groupCategories:20D08, 20D05, 20D60

8. CMB 2002 (vol 45 pp. 272)

Neusel, Mara D.
 The Transfer in the Invariant Theory of Modular Permutation Representations II In this note we show that the image of the transfer for permutation representations of finite groups is generated by the transfers of special monomials. This leads to a description of the image of the transfer of the alternating groups. We also determine the height of these ideals. Keywords:polynomial invariants of finite groups, permutation representation, transferCategory:13A50

9. CMB 1999 (vol 42 pp. 125)

Smith, Larry
 Modular Vector Invariants of Cyclic Permutation Representations Vector invariants of finite groups (see the introduction for an explanation of the terminology) have often been used to illustrate the difficulties of invariant theory in the modular case: see, \eg., \cite{Ber}, \cite{norway}, \cite{fossum}, \cite{MmeB}, \cite{poly} and \cite{survey}. It is therefore all the more surprising that the {\it unpleasant} properties of these invariants may be derived from two unexpected, and remarkable, {\it nice} properties: namely for vector permutation invariants of the cyclic group $\mathbb{Z}/p$ of prime order in characteristic $p$ the image of the transfer homomorphism $\Tr^{\mathbb{Z}/p} \colon \mathbb{F}[V] \lra \mathbb{F}[V]^{\mathbb{Z}/p}$ is a prime ideal, and the quotient algebra $\mathbb{F}[V]^{\mathbb{Z}/p}/ \Im (\Tr^{\mathbb{Z}/p})$ is a polynomial algebra on the top Chern classes of the action. Keywords:polynomial invariants of finite groupsCategory:13A50
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