Search results for "Norma"

Regularity properties of tug-of-war games and normalized equations

2017

Abelian Sylow subgroups in a finite group, II

2015

Abstract Let p ≠ 3 , 5 be a prime. We prove that Sylow p-subgroups of a finite group G are abelian if and only if the class sizes of the p-elements of G are all coprime to p. This gives a solution to a problem posed by R. Brauer in 1956 (for p ≠ 3 , 5 ).

ON SYLOW NORMALIZERS OF FINITE GROUPS

2013

[EN] The paper considers the influence of Sylow normalizers, i.e. normalizers of Sylow subgroups, on the structure of finite groups. In the universe of finite soluble groups it is known that classes of groups with nilpotent Hall subgroups for given sets of primes are exactly the subgroup- closed saturated formations satisfying the following property: a group belongs to the class if and only if its Sylow normalizers do so. The paper analyzes the extension of this research to the universe of all finite groups.

On second minimal subgroups of Sylow subgroups of finite groups

2011

A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids its chief factors. Partial cover and avoidance property has turned out to be very useful to clear up the group structure. In this paper, finite groups in which the second minimal subgroups of their Sylow p-subgroups, p a fixed prime, are partial CAP-subgroups are completely classified.

The average number of Sylow subgroups of a finite group

2013

We prove that if the average Sylow number (ignoring the Sylow numbers that are one) of a finite group G is ⩽7, then G is solvable.

A note on Sylow permutable subgroups of infinite groups

2014

Abstract A subgroup A of a periodic group G is said to be Sylow permutable, or S-permutable, subgroup of G if A P = P A for all Sylow subgroups P of G. The aim of this paper is to establish the local nilpotency of the section A G / Core G ( A ) for an S-permutable subgroup A of a locally finite group G.

On some classes of supersoluble groups

2007

[EN] Finite groups G for which for every subgroup H and for all primes q dividing the index |G:H| there exists a subgroup K of G such that H is contained in K and |K:H|=q are called Y-groups. Groups in which subnormal subgroups permute with all Sylow subgroups are called PST-groups. In this paper a local version of the Y-property leading to a local characterisation of Y-groups, from which the classical characterisation emerges, is introduced. The relationship between PST-groups and Y-groups is also analysed.

Finite groups with all minimal subgroups solitary

2016

We give a complete classification of the finite groups with a unique subgroup of order p for each prime p dividing its order. All the groups considered in this paper will be finite. One of the most fruitful lines in the research in abstract group theory during the last years has been the study of groups in which the members of a certain family of subgroups satisfy a certain subgroup embedding property. The family of the subgroups of prime order (also called minimal subgroups) has attracted the interest of many mathematicians. For example, a well-known result of Itˆo (see [8, Kapitel III, Satz 5.3; 9]) states that a group of odd order with all minimal subgroups in the center is nilpotent. Th…

On the Frattini subgroup of a finite group

2016

We study the class of finite groups $G$ satisfying $\Phi (G/N)= \Phi(G)N/N$ for all normal subgroups $N$ of $G$. As a consequence of our main results we extend and amplify a theorem of Doerk concerning this class from the soluble universe to all finite groups and answer in the affirmative a long-standing question of Christensen whether the class of finite groups which possess complements for each of their normal subgroups is subnormally closed.

Il parco dei Re. Studi sul paesaggio di Palermo nel medioevo

2022

Il volume contiene i primi esiti di una ricerca in corso di svolgimento presso il Dipartimento di Architettura dell’Università degli Studi di Palermo, in partenariato con il Consejo Superior de Investigaciones Científicas Escuela de Estudios Árabes in Granada (Spagna) e la collaborazione della Soprintendenza Regionale ai Beni Culturali e all’Identità Siciliana per la Provincia di Palermo. The volume contains the first results of an ongoing research at the Department of Architecture of the University of Palermo, in partnership with the Consejo Superior de Investigaciones Científicas Escuela de Estudios Árabes in Granada (Spain) and the collaboration of Regional Superintendency for Cultural H…