Search results for "Subgroup"

Existentially closed locally cofinite groups

1992

Let be a class of finite groups. Then a c-group shall be a topological group which has a fundamental system of open neighbourhoods of the identity consisting of normal subgroups with -factor groups and trivial intersection. In this note we study groups which are existentially closed (e.c.) with respect to the class Lc of all direct limits of c-groups (where satisfies certain closure properties). We show that the so-called locally closed normal subgroups of an e.c. Lc-group are totally ordered via inclusion. Moreover it turns out that every ∀2-sentence, which is true for countable e.c. L-groups, also holds for e.c. Lc-groups. This allows it to transfer many known properties from e.c. L-group…

Primitive characters of subgroups ofM-groups

1995

One of the hardest areas in the Character Theory of Solvable Groups continues to be the monomial groups. A finite group is said to be an M-group (or monomial) if all of its irreducible characters are monomial, that is to say, induced from linear characters. Two are still the main problems on M-groups: are Hall subgroups of M groups monomial? Under certain oddness hypothesis, are normal subgroups of M-groups monomial? In both cases there is evidence that this could be the case: the primitive characters of the subgroups in question are the linear characters. This is the best result up to date ([4], [6]). Recently, some idea appears to be taking form. In [14], T. Okuyama proved that if G is an…

A note on character degrees ofp-groups and their normal subgroups

1992

NONVANISHING ELEMENTS FOR BRAUER CHARACTERS

2015

Let $G$ be a finite group and $p$ a prime. We say that a $p$-regular element $g$ of $G$ is $p$-nonvanishing if no irreducible $p$-Brauer character of $G$ takes the value $0$ on $g$. The main result of this paper shows that if $G$ is solvable and $g\in G$ is a $p$-regular element which is $p$-nonvanishing, then $g$ lies in a normal subgroup of $G$ whose $p$-length and $p^{\prime }$-length are both at most 2 (with possible exceptions for $p\leq 7$), the bound being best possible. This result is obtained through the analysis of one particular orbit condition in linear actions of solvable groups on finite vector spaces, and it generalizes (for $p>7$) some results in Dolfi and Pacifici [‘Zero…

Infinite factorized groups

1989

Normalities and Commutators

2010

We first compare several algebraic notions of normality, from a categorical viewpoint. Then we introduce an intrinsic description of Higgins' commutator for ideal-determined categories, and we define a new notion of normality in terms of this commutator. Our main result is to extend to any semi-abelian category the following well-known characterization of normal subgroups: a subobject K is normal in A if. and only if, {[A, K] <= K. (C) 2010 Elsevier Inc. All rights reserved.}

On the p-length of some finite p-soluble groups

2014

The main aim of this paper is to give structural information of a finite group of minimal order belonging to a subgroup-closed class of finite groups and whose $p$-length is greater than $1$, $p$ a prime number. Alternative proofs and improvements of recent results about the influence of minimal $p$-subgroups on the $p$-nilpotence and $p$-length of a finite group arise as consequences of our study

Affine Surfaces With a Huge Group of Automorphisms

2013

We describe a family of rational affine surfaces S with huge groups of automorphisms in the following sense: the normal subgroup Aut(S)alg of Aut(S) generated by all algebraic subgroups of Aut(S) is not generated by any countable family of such subgroups, and the quotient Aut(S)/Aut(S)alg cointains a free group over an uncountable set of generators.

Deep MRD profiling defines outcome and unveils different modes of treatment resistance in standard- and high-risk myeloma

2021

PETHEMA/GEM Cooperative Group.

Short, full-dose neoadjuvant chemotherapy in localized high-risk adult soft tissue sarcomas (STS): An exploratory subgroup analysis on responding pat…

2018

11558Background: We already reported (Cancer 2012;118:5857) the correlation of Choi criteria (Choi) and RECIST with outcome of pts affected by high-risk STS entering a multicentric Italian/Spanish ...