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Displaying 121 –
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A power digraph modulo , denoted by , is a directed graph with as the set of vertices and as the edge set, where and are any positive integers. In this paper we find necessary and sufficient conditions on and such that the digraph has at least one isolated fixed point. We also establish necessary and sufficient conditions on and such that the digraph contains exactly two components. The primality of Fermat number is also discussed.
Let be a finite group, and let be the set of conjugacy class sizes of . By Thompson’s conjecture, if is a finite non-abelian simple group, is a finite group with a trivial center, and , then and are isomorphic. Recently, Chen et al. contributed interestingly to Thompson’s conjecture under a weak condition. They only used the group order and one or two special conjugacy class sizes of simple groups and characterized successfully sporadic simple groups (see Li’s PhD dissertation). In...
An endomorphism f of an Abelian group A is said to be inessentia! (in the category of Abelian groups) if it can be extended to an endomorphism of any Abelian group which contains A as a subgroup. In this paper we show that f is as above if and only if (f - v idA)(A) is contained in the rnaximal divisible subgroup of A for some v belonging to Z.
In survival studies and life testing, the data are generally truncated. Recently, authors have studied a weighted version of Kerridge inaccuracy measure for truncated distributions. In the present paper we consider weighted residual and weighted past inaccuracy measure and study various aspects of their bounds. Characterizations of several important continuous distributions are provided based on weighted residual (past) inaccuracy measure.
We investigate the structure and properties of -sub-semihypergroups, where is an arbitrary triangular norm on a given complete lattice . We study its structure under the direct product and with respect to the fundamental relation. In particular, we consider and , and investigate the connection between -sub-semihypergroups and the probability space.
We characterize totally ordered sets within the class of all ordered sets containing at least three-element chains using a simple relationship between their isotone transformations and the so called 2-, 3-, 4-endomorphisms which are introduced in the paper. Another characterization of totally ordered sets within the class of ordered sets of a locally finite height with at least four-element chains in terms of the regular semigroup theory is also given.
Let be a finite group and construct a graph by taking as the vertex set of and by drawing an edge between two vertices and if is cyclic. Let be the set consisting of the universal vertices of along the identity element. For a solvable group , we present a necessary and sufficient condition for to be nontrivial. We also develop a connection between and when is divisible by two distinct primes and the diameter of is 2.
In this paper, we give some theorems which characterize the intraregular semigroups in terms of intuitionistic fuzzy left, right, and biideals.
Let be a finite group. Let be the first column of the ordinary character table of . We will show that if , then . As a consequence, we show that the projective general unitary groups are uniquely determined by the structure of their complex group algebras.
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