Expand all Collapse all | Results 1 - 8 of 8 |
1. CMB Online first
$m$-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 subgroup Categories:20D10, 20D15 |
2. CMB 2013 (vol 57 pp. 125)
Camina Triples In this paper, we study Camina triples. Camina triples are a
generalization of Camina pairs. Camina pairs were first introduced
in 1978 by A .R. Camina.
Camina's work
was inspired by the study of Frobenius groups. We
show that if $(G,N,M)$ is a Camina triple, then either $G/N$ is a
$p$-group, or $M$ is abelian, or $M$ has a non-trivial nilpotent or
Frobenius quotient.
Keywords:Camina triples, Camina pairs, nilpotent groups, vanishing off subgroup, irreducible characters, solvable groups Category:20D15 |
3. CMB 2012 (vol 56 pp. 606)
Characterization of Simple Highest Weight Modules We prove that for simple complex finite dimensional
Lie algebras, affine Kac-Moody Lie algebras, the
Virasoro algebra and the Heisenberg-Virasoro algebra,
simple highest weight modules are characterized
by the property that all positive root elements
act on these modules locally nilpotently. We
also show that this is not the case for higher rank
Virasoro and for Heisenberg algebras.
Keywords:Lie algebra, highest weight module, triangular decomposition, locally nilpotent action Categories:17B20, 17B65, 17B66, 17B68 |
4. CMB 2011 (vol 55 pp. 579)
Casimir Operators and Nilpotent Radicals It is shown that a Lie algebra having a nilpotent radical has a
fundamental set of invariants consisting of Casimir operators. A
different proof is given in the well known special case of an
abelian radical. A result relating the number of invariants to the
dimension of the Cartan subalgebra is also established.
Keywords:nilpotent radical, Casimir operators, algebraic Lie algebras, Cartan subalgebras, number of invariants Categories:16W25, 17B45, 16S30 |
5. CMB 2009 (vol 52 pp. 535)
A Note on Locally Nilpotent Derivations\\ and Variables of $k[X,Y,Z]$ We strengthen certain results
concerning actions of $(\Comp,+)$ on $\Comp^{3}$
and embeddings of $\Comp^{2}$ in $\Comp^{3}$,
and show that these results are in fact valid
over any field of characteristic zero.
Keywords:locally nilpotent derivations, group actions, polynomial automorphisms, variable, affine space Categories:14R10, 14R20, 14R25, 13N15 |
6. CMB 2004 (vol 47 pp. 343)
Combinatorics of Words and Semigroup Algebras Which Are Sums of Locally Nilpotent Subalgebras We construct new examples of non-nil algebras with any number of
generators, which are direct sums of two
locally nilpotent subalgebras. Like all previously known examples, our examples
are contracted semigroup algebras and the underlying semigroups are unions
of locally nilpotent subsemigroups.
In our constructions we make more
transparent
than in the past the close relationship between the considered problem
and combinatorics of words.
Keywords:locally nilpotent rings,, nil rings, locally nilpotent semigroups,, semigroup algebras, monomial algebras, infinite words Categories:16N40, 16S15, 20M05, 20M25, 68R15 |
7. CMB 2001 (vol 44 pp. 266)
Extension of Maps to Nilpotent Spaces We show that every compactum has cohomological dimension $1$ with respect
to a finitely generated nilpotent group $G$ whenever it has cohomological
dimension $1$ with respect to the abelianization of $G$. This is applied
to the extension theory to obtain a cohomological dimension theory condition
for a finite-dimensional compactum $X$ for extendability of every map from
a closed subset of $X$ into a nilpotent $\CW$-complex $M$ with finitely
generated homotopy groups over all of $X$.
Keywords:cohomological dimension, extension of maps, nilpotent group, nilpotent space Categories:55M10, 55S36, 54C20, 54F45 |
8. CMB 1999 (vol 42 pp. 335)
Cyclic Subgroup Separability of HNN-Extensions with Cyclic Associated Subgroups We derive a necessary and sufficient condition for HNN-extensions
of cyclic subgroup separable groups with cyclic associated
subgroups to be cyclic subgroup separable. Applying this, we
explicitly characterize the residual finiteness and the cyclic
subgroup separability of HNN-extensions of abelian groups with
cyclic associated subgroups. We also consider these residual
properties of HNN-extensions of nilpotent groups with cyclic
associated subgroups.
Keywords:HNN-extension, nilpotent groups, cyclic subgroup separable $(\pi_c)$, residually finite Categories:20E26, 20E06, 20F10 |