In this paper we study generic expansions of predicate logics of some left-continuous t-norms (mainly Gödel and Nilpotent Minimum predicate logics) with a countable set of truth-constants. Using known results on tnorm based predicate fuzzy logics we obtain results on the conservativeness and completeness for the expansions of some predicate fuzzy logics. We describe the problem for the cases of...

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...

In this paper, the intuitionistic fuzzy Lie sub-superalgebras and ideals of Lie superalgebras are studied further. We define the intuitionistic fuzzy quotient Lie superalgebra by an intuitionistic fuzzy Lie ideal and prove that it is a Lie superalgebra. The intuitionistic fuzzy set of quotient Lie superalgebra is also considered. Finally, solvable intuitionistic fuzzy Lie ideals and nilpotent i...

The punctured power graph P (G) of a finite group G is the graph which has as vertex set the nonidentity elements of G, where two distinct elements are adjacent if one is a power of the other. We show that P (G) has diameter at most 2 if and only if G is nilpotent and every Sylow subgroup of G is either a cyclic group or a generalized quaternion 2-group. Also, we show that if G is a finite grou...

Continuing our recent research on embedding properties of generalized soluble and generalized nilpotent groups, we study some embedding properties of SD-groups. We show that every countable SD-group G can be subnormally embedded into a two-generator SD-group H. This embedding can have additional properties: if the group G is fully ordered, then the group H can be chosen to be also fully ordered...

In this paper we investigate expanding maps on infra-nilmanifolds. Such manifolds are obtained as a quotient E\L, where L is a connected and simply connected nilpotent Lie group and E is a torsion-free uniform discrete subgroup of LoC, with C a compact subgroup of Aut(L). We show that if the Lie algebra of L is homogeneous (i.e., graded and generated by elements of degree 1), then the correspon...

We establish a surprising correspondence between groups definable in o-minimal structures and linear algebraic groups, the nilpotent case. It turns out that context, like for finite nilpotency is equivalent to normalizer property or uniqueness of Sylow subgroups, provided maximal normal torsion-free subgroup nilpotent. As consequence, we show decompositions prove Lie group an expansion reals if...

This article examines aspects of the theory of locally nilpotent linear groups. We also present a new classification result for locally nilpotent linear groups over an arbitrary field F. 1. Why Locally Nilpotent Linear Groups? Linear (matrix) groups are a commonly used concrete representation of groups. The first investigations of linear groups were undertaken in the second half of the 19th cen...

There exists a generalization of the Teichmüller space of a covering group. In this paper we combine this generalized Teichmüller space T (G) and any fuzzy subgroup A : G−→ F where G is a subgroup of the group consisting of such orientation preserving and orientation reversing Möbius transformations which act in the upper half-plane of the extended complex plane. A partially ordered set F = (F ...