This paper is concerned with finite primitive permutation groups G which are subgroups of wreath products W in product action and are such that the socles of G and W are the same. The aim is to explore how the study of such groups may be reduced to the study of smaller groups. The O'Nan-Scott Theorem (see Liebeck, Praeger, Saxl [12] for the most recent and detailed treatment) sorts finite primi...

The wreath product of groups A B is one of basic constructions in group theory. We construct its analogue, a wreath product of Lie algebras. Consider Lie algebras H and G over a field K. Let U(G) be the universal enveloping algebra. Then H̄ = HomK(U(G), H) has the natural structure of a Lie algebra, where the multiplication is defined via the comultiplication in U(G). Also, G acts by derivations...

We study Euler–Poincaré systems (i.e., the Lagrangian analogue of LiePoisson Hamiltonian systems) defined on semidirect product Lie algebras. We first give a derivation of the Euler–Poincaré equations for a parameter dependent Lagrangian by using a variational principle of Lagrange d’Alembert type. Then we derive an abstract Kelvin-Noether theorem for these equations. We also explore their rela...

After developing a theory of implicit operations and proving an analogue of Reiterman's theorem for categories, this paper addresses two complementary questions for semidirect products and two-sided semidirect products of pseudovarieties of semigroups: to determine when a pseudoidentity is valid in it, and to nd a basis of pseudoidentities. The rst question involves looking into the structure o...

The construction of continuous shearlet transform has been extended to higher dimensions. It was generalized a group that is topologically isomorphic semidirect product locally compact groups. In this paper, by unified theoretical linear algebra approach the representation theory, class transforms obtained from quasi-regular presented. order develop such representation, we utilize homogeneous s...

For a non-empty set X denote the full transformation semigroup of by T(X). Let \(\sigma\) be an equivalence relation on and E(X, \(\sigma\)) denotes (under composition) all \(\alpha\) : \(\mapsto\) X, such that \(\subseteq\) ker(\(\alpha\) ). Semigroup transformations with restricted occur when we take whose kernel is contained in some fixed equivalence, \(\sigma\)). First, found disjoint union...