Related papers: Conditions for a Schunck class to be a formation

Schunck classes, saturated formations and projectors were originally defined for finite soluble groups for which they provided families of intravariant subgroups. In this paper, I set out the analogous theory for finite-dimensional soluble…

Necessary and sufficient conditions are given for the endomorphism monoid of a profinite semigroup to be profinite. A similar result is established for the automorphism group.

We obtain a necessary and sufficient condition for an algebraic set in a group to have a fully characteristic radical. As a result, we see that if the radical of a system of equation $S$ over a group $G$ is fully characteristic, then there…

Let X=G/P be cominuscule rational homogeneous variety. (Equivalently, X admits the structure of a compact Hermitian symmetric space.) We say a Schubert class [S] is Schur rigid if the only irreducible subvarieties Y of X with homology class…

Necessary and sufficient conditions for finite semihypergroups to be built from groups of the same order are established

A criterion for the HNN-extension of a finite p-group to be residually a finite p-group is obtained and based on this criterion the sufficient condition for residuality a finite p-group of HNN-extension with arbitrary base group is proved.…

In recent years, there has been considerable interest in showing that certain conditions on skew shapes A and B are sufficient for the difference s_A - s_B of their skew Schur functions to be Schur-positive. We determine necessary…

It is shown that, if H,K are saturated formations of soluble Lie algebras over a field of non-zero characteristic and H strongly contains K non-trivially, then H coincides with the formation generated by the L/N(L) for L in H, and that H is…

The topology of a space $X$ is generated by a family $\mathcal{C}$ of its subsets provided that a set $A\subseteq X$ is closed in $X$ if and only if $A\cap C$ is closed in $C$ for each $C\in \mathcal{C}$. A space $X$ is a $k$-space…

It is formally constructed a normal form for a class of real-formal surfaces defined near a CR Singularity.

Let Z be a complex space and let S be a compact set in C^n x Z which is fibered over R^n (the real subspace of C^n). We give a necessary and sufficient condition for S to be a Stein compactum.

Let $\mathfrak{J}$ be a class of non-abelian simple groups and $\mathfrak{X}$ be a class of groups. A chief factor $H/K$ of a group $G$ is called $\mathfrak{X}$-central in $G$ provided $(H/K)\rtimes G/C_G(H/K)\in\mathfrak{X}$. We say that…

The structure of solutions is studied for the Lax equation $D_t(G)=[F,G]$ for formal power series with respect to the shift operator. It is proved that if the equation with a given series $F$ of degree $m$ admits a solution $G$ of degree…

An object in the bounded derived category D^b(Coh(X)) of coherent sheaves on a complex projective K3 surface X is spherical if it is rigid and simple. Although spherical objects form only a discrete set in the moduli stack of complexes,…

Necessary and sufficient conditions are given for the existence of extended Schmidt decompositions, with more than two subspaces.

In this article we calculate the profinite genus of the fundamental group of a $n$-dimensional compact flat manifold $X$ with holonomy group of prime order. As consequence, we prove that if $n\leq 21$, then $X$ is determined among all…

Let $d(G)$ be the minimum number of elements required to generated a group $G.$ For a group $G $ of order $p^n$ with derived subgroup of order $ p^k $ and $d(G) = d,$ we knew the order of the Schur multiplier of $G$ is bounded by $…

An $integral$ of a group $G$ is a group $H$ whose commutator subgroup is isomorphic to $G$. This paper continues the investigation on integrals of groups started in the work arXiv:1803.10179. We study: (1) A sufficient condition for a bound…

We establish the structure of finite groups with $\mathfrak{F}$-subnormal or self-normalizing primary cyclic subgroups in case $\mathfrak{F}$ is a subgroup-closed saturated superradical formation containing all nilpotent groups.

Necessary and sufficient conditions for the internal stability of formations whose dynamics are obtained is determined by linear differential equations.