We study a class of $\mathbb{Z}^{d}$-substitution subshifts, including large family constant-length substitutions, and homomorphisms between them, i.e., factors modulo isomorphisms $\mathbb{Z}^{d}$. prove that any measurable factor even homomorphism associated to matrix commuting with the expansion matrix, induced continuous one. also get strong restrictions on normalizer group, proving endomor...

In this thesis we primarily consider saturated fusion systems which are of essential rank 1, i.e. which contain only one conjugacy class of essential subgroups. We prove that they all can be realized by an amalgam of two finite groups. This leads us to the application of amalgam related methods like pushing up techniques and results about FF-modules. As a first key result, in fusion systems of ...

The notion of p-compact group [10] is a homotopy theoretic version of the geometric or analytic notion of compact Lie group, although the homotopy theory differs from the geometry is that there are parallel theories of p-compact groups, one for each prime number p. A key feature of the theory of compact Lie groups is the relationship between centers and fundamental groups; these play off agains...

In this paper, we settle an open conjecture regarding the assertion that Euler-characteristic of G/NG(T) for a split reductive group scheme G and normalizer maximal torus NG(T) over field is 1 in Grothendieck-Witt ring with characteristic exponent inverted, under assumption base contains −1. Numerous applications to splittings motivic stable homotopy category Algebraic K-Theory are worked out s...

The article substantiates the possibility of using spices in soft goat cheese technology. For production cheeses, black pepper, garlic and red pepper are selected, which have an antiseptic effect, used for intestinal disorders, myositis, rheumatism, polyarthritis, atherosclerosis, gout, anemia, hypertension, angina pectoris bronchial asthma. process preparing fillers before adding them to mass ...

an algebraic construction for constant dimension subspace codes is called orbit code. it arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. in particular orbit codes of a singer subgroup of the general linear group has investigated recently. in this paper, we consider the normalizer of a singer subgroup of the general linear group a...

The general problem of computing the normalizer, in a finite permutat ion group G, of a subgroup H has long been recognized as being unusually difficult to solve efficiently. The corresponding problem for centralizers is much easier, although this too has some bad cases. The solution to the centralizer problem is relatively simple and probably difficult to improve upon, whereas there seems to b...

Let N N be the normalizer of a maximal torus T"> T encoding="application/x-tex">T in split reductive ...

On the basis of an initial interest in symmetric cryptography, present work we study a chain subgroups. Starting from Sylow $2$-subgroup AGL(2,n), each term is defined as normalizer previous one group on $2^n$ letters. Partial results and computational experiments lead us to conjecture that, for large values $n$, index consecutive does not depend $n$. Indeed, there strong evidence that sequence...