Criteria for $ \sigma $ -Solvability and Meta- $ \sigma $ -Nilpotency of a Finite Group

Siberian Mathematical Journal - We study some conditions for a group to be $ \sigma $ -solvable or meta- $ \sigma $ -nilpotent.     

On $ \sigma $ -Subnormality of Sylow Subgroups in a Finite Group

Siberian Mathematical Journal - Given an arbitrary partition  $ \sigma $ of the set of primes, we give some criteria for the $ \sigma $ -subnormality of a Sylow subgroup of...     

On Intersections of $ pi $ -Hall Subgroups in Finite $ D_{pi} $ -Groups

Siberian Mathematical Journal - We give an example of a series of finite $ D_{pi} $ -groups where for each group $ G $ in the series and its $ pi $ -Hall subgroup $ H $ , the inequality $ Hcap...     

Representations,Products, and Varieties of $ m $ -Groups

Siberian Mathematical Journal - Under study is the structure of the $ m $ -homomorphic images of $ m $ -subgroups in a Cartesian product of $ m $ -groups which admit a faithful $ m $...     

$\mathcal{P}$-kernel normal systems for $\mathcal{P}$-inversive semigroups

As a generalization of Preston’s kernel normal systems, P\mathcal{P}-kernel normal systems for P\mathcal{P}-inversive semigroups are introduced, and strongly regular P\mathcal{P}-congruences on P\mathcal{P}-inversive semigroups in terms of their P\mathcal{P}-kernel normal systems are characterized. These results generalize the corresponding results for P\mathcal{P}-regular semigroups and P\mathcal{P}-inversive semigroups.     

The size of $\tilde{T}$

Given a stationary subset T of , let be the set of ordinals in the interval which are necessarily in the image of T by any embedding derived from the nonstationary ideal. We consider the question of the size of , givenT, and use Martin's Maximum and to give some answers. Received: 23 November 1998     

On Commuting Automorphisms of Finite $$p$$ -Groups

Mathematical Notes -     

Finite 2-Groups with Automorphisms of Order 4

It is proved that if a locally finite or locally nilpotent 2-group G admits an automorphism of order 4 with finitely many fixed points m then G possesses a normal subgroup H of m-bounded index such that the second derived subgroup of H is contained in its center.     

A new kind of triangular integrals based on $\mathfrak{T}$-norms and $\mathfrak{T}$-conorms

Fuzzy integrals are commonly used as aggregation operators. In this paper, we present a new model based on fuzzy integrals with \mathfrakT\mathfrak{T}-norms and \mathfrakT\mathfrak{T}-conorms before obtaining some basic properties. This model can act as an aggregation tool to deal with many information fusing and data mining problems such as programming and classification.     

Finite groups with \mathbb{P }-subnormal subgroups

A subgroup $H$ of a group $G$ is called $\mathbb{P }$ -subnormal in $G$ whenever either $H=G$ or there is a chain of subgroups $H=H_0\subset H_1\subset \cdots \subset H_n=G$ such that $|H_i:H_{i-1}|$  is a prime for all $i$ . In this paper we study groups with $\mathbb{P }$ -subnormal 2-maximal subgroups, and groups with $\mathbb{P }$ -subnormal primary cyclic subgroups.     

A Criterion for Binarity of Almost $ omega $ -Categorical Weakly $ o $ -Minimal Theories

Siberian Mathematical Journal - Continuing the study of weak $ o $ -minimality, we prove a theorem on the behavior of a definable unary function on the set of realizations of a nonalgebraic 1-type...     

Almost $ \omega $ -Categorical Weakly $ o $ -Minimal Theories of Convexity Rank 1

Siberian Mathematical Journal - Studying the properties of almost $ \omega $ -categorical weakly $ o $ -minimal theories of convexity rank 1, we prove the orthogonality of every family of...     

New exact solutions of two-dimensional integrable equations using the $\bar \partial $-dressing method

We review new classes of exact solutions with functional parameters with constant asymptotic values at infinity of the Nizhnik-Veselov-Novikov equation and new classes of exact solutions with functional parameters of two-dimensional generalizations of the Kaup-Kupershmidt and Sawada-Kotera equations, constructed using the Zakharov-Manakov \(\bar \partial \)-dressing method. We present subclasses of multisoliton and periodic solutions of these equations and give examples of linear superpositions of exact solutions of the Nizhnik-Veselov-Novikov equation.     

Lipschitzian Properties of Integral Functionals on Lebesgue Spaces $\bf{L_p, 1 \leqslant {p} < \infty}$

We give complete characterizations of integral functionals which are Lipschitzian on a Lebesgue space L _p with p ≠ ∞. When the measure is atomless, we characterize the integral functionals which are locally Lipschitzian on such Lebesgue spaces. In every cases, the Lipchitzian properties of the integral functional can be described by growth conditions on the subdifferentials of the integrand which are equivalent to Lipschitzian properties of the integrand.     

Deformation of the $$\sigma _2$$-curvature

Our main goal in this work is to deal with results concern to the \(\sigma _2\)-curvature. First we find a symmetric 2-tensor canonically associated to the \(\sigma _2\)-curvature and we present an almost-Schur-type lemma. Using this tensor, we introduce the notion of \(\sigma _2\)-singular space and under a certain hypothesis we prove a rigidity result. Also we deal with the relations between flat metrics and \(\sigma _2\)-curvature. With a suitable condition on the \(\sigma _2\)-curvature, we show that a metric has to be flat if it is close to a flat metric. We conclude this paper by proving that the three-dimensional torus does not admit a metric with constant scalar curvature and nonnegative \(\sigma _2\)-curvature unless it is flat.