On an open problem about π-quasi-F-groups
نویسندگان
چکیده
Let F be a class of finite groups, p a prime and π a set of some primes. A finite group G is called a p-quasi-F-group (respectively, by π-quasi-F-group) provided that for every F-eccentric G-chief factor H/K of order divisible by p (respectively, by at least one prime in π), the automorphisms of H/K induced by all elements of G are inner. In this paper, we obtain the characterizations of p-quasi-F-groups and π-quasi-F-groups, which give a positive answer to an open problem in the book [3]. Mathematics Subject Classification (2010). 20D10, 20D15, 20D20
منابع مشابه
A note on quasi irresolute topological groups
In this study, we investigate the further properties of quasi irresolute topological groups defined in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connected quasi irresolute topological group $(G,*,tau )$, if $V$ is any symmetric semi-open neighborhood of $e_G$, then...
متن کاملTheoretical study of the effects of substituent and quadrupole moment on π-π stacking interactions with coronene
Stability of the π-π stacking interactions in the Ben||substituted-coronene and HFBen||substituted-coronene complexes was studied using the computational quantum chemistry methods (where Ben and HFBen are benzene and hexaflourobenzene, || denotes π-π stacking interaction, substituted-coronene is coronene molecule which substituted with four X groups, and X= NH2, CH3, OH, H, F, CF3, CN and NO). ...
متن کاملWhittaker Supports for Representations of Reductive Groups
Let F be either R or a finite extension of Qp, and let G be a finite central extension of the group of F -points of a reductive group defined over F . Also let π be a smooth representation of G (Fréchet of moderate growth if F = R). For each nilpotent orbit O we consider a certain Whittaker quotient πO of π. We define the Whittaker support WS(π) to be the set of maximal O among those for which ...
متن کاملAN EXPLICIT CONDUCTOR FORMULA FOR GL(n)×GL(1) AND FUNCTORIAL DEPTH PRESERVATION
We prove an explicit formula for the conductor of an irreducible, admissible representation of GL(n, F ) twisted by a character of F× where the field F is local and non-archimedean. The components of our formula are analysed, both explicitly and on average, for application to the analytic study of automorphic forms on GL(n). We also demonstrate that “functoriality preserves depth” for such Rank...
متن کاملQuasi-polynomial Hitting-set for Set-depth-Delta Formulas
We call a depth-4 formula C set-depth-4 if there exists a (unknown) partition X1 t · · · t Xd of the variable indices [n] that the top product layer respects, i.e. C(x) = ∑k i=1 ∏d j=1 fi,j(xXj ), where fi,j is a sparse polynomial in F[xXj ]. Extending this definition to any depth we call a depth-∆ formula C (consisting of alternating layers of Σ and Π gates, with a Σ-gate on top) a set-depth-∆...
متن کامل