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Let $G$ be a group and $p$ a prime. The subgroup generated by the elements of order different from $p$ is called the Hughes subgroup for exponent $p$ . Hughes [3] made the following conjecture: if $H_{p} (G)$ is non-trivial, its index in $G$ is at most $p$ . There are many articles that treat this problem. In the present Note we examine those of Strauss and Szekeres [9], which treats the case $p = 3$ and $G$ arbitrary, and that of Hogan and Kappe [2] concerning the case when $G$ is metabelian, and $p$ arbitrary. A common proof is...

The independence number of a subset of an Abelian group.

Bajnok, Béla, Ruzsa, Imre (2003)

Integers

The influence of weakly-supplemented subgroups on the structure of finite groups

Qingjun Kong, Qingfeng Liu (2014)

Czechoslovak Mathematical Journal

A subgroup $H$ of a finite group $G$ is weakly-supplemented in $G$ if there exists a proper subgroup $K$ of $G$ such that $G = H K$ . In the paper it is proved that a finite group $G$ is $p$ -nilpotent provided $p$ is the smallest prime number dividing the order of $G$ and every minimal subgroup of $P \cap G^{'}$ is weakly-supplemented in $N_{G} (P),$ where $P$ is a Sylow $p$ -subgroup of $G$ . As applications, some interesting results with weakly-supplemented minimal subgroups of $P \cap G^{'}$ are obtained.

The Join of Two Fitting Classes.

Elspeth Cusack (1979)

Mathematische Zeitschrift

The lattice of equational theories. Part I: Modular elements

Jaroslav Ježek (1981)

Czechoslovak Mathematical Journal

The lattice of Fitting classes which are right extensible by soluble groups.

M.J. Iranzo, Julio P. Lafuente, F. Pérez-Monasor (2005)

Publicacions Matemàtiques

In this paper we study the set of Fitting classes which are right extensible by soluble groups ordered by the inclusion relation. The consideration of the associated lattices gives rise to new Fitting classes and it allows to obtain some injectivity criteria for general Fitting classes.

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The Fitting class generated by the $π$ -perfect groups

The formation generated by a finite group

The Friendly Giant.

The function g(h) for which |A(G)|p>=p^h whenever |G|>=p^g(h) , G a finite P-group

The generalized commutativity degree in a finite group.

The groups of order at most 2000.

The Hughes subgroup

The independence number of a subset of an Abelian group.

The influence of weakly-supplemented subgroups on the structure of finite groups

The Join of Two Fitting Classes.

The lattice of equational theories. Part I: Modular elements

The lattice of Fitting classes which are right extensible by soluble groups.

The lattice of very-well-placed subgroups

The Mathieu group $M_{12}$ and its pseudogroup extension $M_{13}$ .

The maximum distinguishing number of a group.

The maximum order of finite groups of outer automorphisms of free groups.

The Minimal 5-Representation of Lyon's Sporadic Group.

The number of conjugacy classes in a finite nilpotent group

The number of finite groups whose element orders is given.

The number of k-sums of abelian groups of order k

Currently displaying 961 – 980 of 1356