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On lattice properties of S-permutably embedded subgroups of finite soluble groups

L. M. Ezquerro, M. Gómez-Fernández, X. Soler-Escrivà (2005)

Bollettino dell'Unione Matematica Italiana

In this paper we prove the following results. Let π be a set of prime numbers and G a finite π-soluble group. Consider U, V ≤ G and $H \in {Hall}_{π} (G)$ such that $H \cap V \in {Hall}_{π} (V)$ and $1 \neq H \cap U \in {Hall}_{π} (U)$ . Suppose also $H \cap U$ is a Hall π-sub-group of some S-permutable subgroup of G. Then $H \cap U \cap V \in {Hall}_{π} (U \cap V)$ and $〈 H \cap U, H \cap V 〉 \in {Hall}_{π} (〈 U \cap V 〉)$ . Therefore,the set of all S-permutably embedded subgroups of a soluble group G into which a given Hall system Σ reduces is a sublattice of the lattice of all Σ-permutable subgroups of G. Moreover any two subgroups of this sublattice of coprimeorders permute.

On loops that are abelian groups over the nucleus and Buchsteiner loops

Piroska Csörgö (2008)

Commentationes Mathematicae Universitatis Carolinae

We give sufficient and in some cases necessary conditions for the conjugacy closedness of $Q / Z (Q)$ provided the commutativity of $Q / N$ . We show that if for some loop $Q$ , $Q / N$ and $Inn Q$ are abelian groups, then $Q / Z (Q)$ is a CC loop, consequently $Q$ has nilpotency class at most three. We give additionally some reasonable conditions which imply the nilpotency of the multiplication group of class at most three. We describe the structure of Buchsteiner loops with abelian inner mapping groups.

On loops whose inner permutations commute

Piroska Csörgö, Tomáš Kepka (2004)

Commentationes Mathematicae Universitatis Carolinae

Multiplication groups of (finite) loops with commuting inner permutations are investigated. Special attention is paid to the normal closure of the abelian permutation group.

Our aim is to determine necessary and sufficient conditions for a finite nilpotent group to have a faithful irreducible projective representation over a field of characteristic p ≥ 0.

Currently displaying 101 – 120 of 242

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Displaying 101 – 120 of 242

On lattice properties of S-permutably embedded subgroups of finite soluble groups

On loops that are abelian groups over the nucleus and Buchsteiner loops

On loops whose inner permutations commute

On minimal factorisations of sporadic groups.

On minimal length factorizations of finite groups.

On minimal logarithmic signatures of finite groups.

On minimal non-supersoluble groups.

On minimal permutation representations of classical simple groups.

On minimal subgroups which are normal.

On modular projective representations of finite nilpotent groups

On monomial p...-representations of finite p-groups.

On nonnilpotent groups in which every two 3-maximal subgroups are permutable.

On Normal Subgroups of p-Solvable Groups.

On n-Sum Groups.

On numbers with a unique representation by a binary quadratic form

On orbits of automorphism groups.

On Outer Automorphism Groups.

On $p$ -decomposable groups.

On $p$ -groups whose $L$ -automorphism group is transitive on the atoms

On $p$ -groups with abelian automorphism group

Currently displaying 101 – 120 of 242