A k-nacci （k-step Fibonacci） sequence in a finite group is a sequence of group elements x0,x1,x2,...,xn,.., for which, given an initial （seed） set x0,x1,x2,...,xj-1, each element is defined by xn{x0x1…xn-1 forj≤...A k-nacci （k-step Fibonacci） sequence in a finite group is a sequence of group elements x0,x1,x2,...,xn,.., for which, given an initial （seed） set x0,x1,x2,...,xj-1, each element is defined by xn{x0x1…xn-1 forj≤n〈k xn-kxn-k＋1 …xn-1 for n≥kFrom the definition, it is clear that the period of the k-nacci sequence in a group depends on the chosen generating set and the order in which the assignments of x0, x1, x2,…~, xj-1 are made. In this paper we examine the periods of the k-nacci sequences in the groups m2, m2＋ and R2, where each term of the sequence is reduced modulo 2.展开更多
In this article, we first investigate the properties of modular Frobenius groups. Then, we consider the case that G＇ is a minimal normal subgroup of a modular Frobenius group G. We give the complete classification of...In this article, we first investigate the properties of modular Frobenius groups. Then, we consider the case that G＇ is a minimal normal subgroup of a modular Frobenius group G. We give the complete classification of G when G＇ as a modular Frobenius kernel has no more than four conjugacy classes in G.展开更多
Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft gr...Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft group is the generalization of soft group. Abdulkadir Aygunoglu and Halis Aygun introduced the notion of fuzzy soft groups in 2009[1]. In this paper, the concept of lattice ordered fuzzy soft groups and its duality has been introduced. Then distributive and modular lattice ordered fuzzy soft groups are analysed. The objective of this paper is to study the lattice theory over the collection of fuzzy soft group in a parametric manner. Some pertinent properties have been analysed and hence established duality principle.展开更多
文摘A k-nacci （k-step Fibonacci） sequence in a finite group is a sequence of group elements x0,x1,x2,...,xn,.., for which, given an initial （seed） set x0,x1,x2,...,xj-1, each element is defined by xn{x0x1…xn-1 forj≤n〈k xn-kxn-k＋1 …xn-1 for n≥kFrom the definition, it is clear that the period of the k-nacci sequence in a group depends on the chosen generating set and the order in which the assignments of x0, x1, x2,…~, xj-1 are made. In this paper we examine the periods of the k-nacci sequences in the groups m2, m2＋ and R2, where each term of the sequence is reduced modulo 2.
基金Supported by the National Natural Science Foundation of China (11171243, 11201385)the Technology Project of Department of Education of Fujian Province(JA12336)+1 种基金the Fundamental Research Funds for the Central Universities (2010121003)the Science and the Natural Science Foundation of Fujian Province (2011J01022)
文摘In this article, we first investigate the properties of modular Frobenius groups. Then, we consider the case that G＇ is a minimal normal subgroup of a modular Frobenius group G. We give the complete classification of G when G＇ as a modular Frobenius kernel has no more than four conjugacy classes in G.
文摘Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft group is the generalization of soft group. Abdulkadir Aygunoglu and Halis Aygun introduced the notion of fuzzy soft groups in 2009[1]. In this paper, the concept of lattice ordered fuzzy soft groups and its duality has been introduced. Then distributive and modular lattice ordered fuzzy soft groups are analysed. The objective of this paper is to study the lattice theory over the collection of fuzzy soft group in a parametric manner. Some pertinent properties have been analysed and hence established duality principle.
