Displaying similar documents to “On finite minimal non-p-supersoluble groups”

On residually finite groups and their generalizations

Andrzej Strojnowski (1999)

Colloquium Mathematicae

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The paper is concerned with the class of groups satisfying the finite embedding (FE) property. This is a generalization of residually finite groups. In [2] it was asked whether there exist FE-groups which are not residually finite. Here we present such examples. To do this, we construct a family of three-generator soluble FE-groups with torsion-free abelian factors. We study necessary and sufficient conditions for groups from this class to be residually finite. This answers the questions...

Sylow 2-subgroups of solvable Q-groups.

Mohammad Reza Darafsheh, H. Sharifi (2007)

Extracta Mathematicae

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A finite group whose irreducible characters are rational valued is called a rational or a Q-group. In this paper we obtain various results concerning the structure of a Sylow 2-subgroup of a solvable Q-group.

On minimal non--groups

Francesco Russo, Nadir Trabelsi (2009)

Annales mathématiques Blaise Pascal

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A group G is said to be a -group, if G / C G ( x G ) is a polycyclic-by-finite group for all x ∈ G . A minimal non--group is a group which is not a -group but all of whose proper subgroups are -groups. Our main result is that a minimal non--group having a non-trivial finite factor group is a finite cyclic extension of a divisible abelian group of finite rank.

On the Olson and the Strong Davenport constants

Oscar Ordaz, Andreas Philipp, Irene Santos, Wolfgang A. Schmid (2011)

Journal de Théorie des Nombres de Bordeaux

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A subset S of a finite abelian group, written additively, is called zero-sumfree if the sum of the elements of each non-empty subset of S is non-zero. We investigate the maximal cardinality of zero-sumfree sets, i.e., the (small) Olson constant. We determine the maximal cardinality of such sets for several new types of groups; in particular, p -groups with large rank relative to the exponent, including all groups with exponent at most five. These results are derived as consequences of...