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We define generalized cluster states based on finite group algebras in analogy to the generalization of the toric code to the Kitaev quantum double models. We do this by showing a general correspondence between systems with CSS structure…
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…
This paper investigates new first-order optimality conditions for general optimization problems. These optimality conditions are stronger than the commonly used M-stationarity conditions and are in particular useful when the latter cannot…
This paper contains a stronger version of a final identification theorem for the `generic' groups of finite Morley rank.
The enhanced group classification of a semi-linear generalization of a general bond-pricing equation is carried out by employing the underlying equivalence and additional equivalence transformations. The knowledge of the sub classes with…
In this note some properties of the sum of element orders of a finite abelian group are studied.
We show that the class of profinite duality groups is closed under group extensions provided that the kernel satisfies some finiteness condition. This extends earlier results of Pletch and of Wingberg.
We calculate the first extension groups for finite-dimensional simple modules over an arbitrary generalized current Lie algebra, which includes the case of loop Lie algebras and their multivariable analogs.
We present an overview of the theory of finite groups, with regard to their application as flavour symmetries in particle physics. In a general part, we discuss useful theorems concerning group structure, conjugacy classes, representations…
In this paper, we discuss some well-known results and some open problems of the theory of $\sigma$-properties of a group related to the study of generalized $T$-groups.
Necessary and sufficient conditions for finite semihypergroups to be built from groups of the same order are established
This paper gives a systematic construction of certain covers of finite semigroups. These covers will be used in future work on the complexity of finite semigroups.
In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…
We establish a sufficient condition for a finitely generated pro-$p$ group to be accessible in terms of finite generation of the module of ends.
Finite groups with given systems of permuteral and strongly permuteral subgroups are studied. New characterizations of w-supersoluble and supersoluble groups are received.
In this paper, we introduce the general fractional integrals and derivatives of arbitrary order and study some of their basic properties and particular cases. First, a suitable generalization of the Sonine condition is presented and some…
We introduce some general and special formulations of general position theorem for parametrized families of fractals and explain the techniques of its application to prove the existence of self-similar sets with prescribed special…
Given a prime power $p^d$ with $p$ a prime and $d$ a positive integer, we classify the finite groups $G$ with $p^{2d}$ dividing $|G|$ in which all subgroups of order $p^d$ are complemented and the finite groups $G$ having a normal…
Using a Zariski topology associated to a finite field extensions, we give new proofs and generalize the primitive and normal basis theorems.
In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion. In particular, spaces of generalized functions are constructed that contain generalized solutions to all systems of continuous,…