The just non-(virtually abelian) groups with non-trivial Fitting subgroup are classified. Particular attention is given to those which are virtually nilpotent and examples are given of the interesting phenomena that can occur.

We give a proof of Gromov’s theorem that any finitely generated group of polynomial growth has a finite index nilpotent subgroup. The proof does not rely on the Montgomery-ZippinYamabe structure theory of locally compact groups.

We prove that any finitely generated solvable group of zero entropy contains a nilpotent subgroup of finite index. In particular, any finitely generated solvable group of exponential growth is of uniformly exponential growth.

We define the fuzzy description logic ALCHNM based on the t-norm of Nilpotent Minimum and we prove its reduction to the crisp description logic ALCH. Hence we prove decidability results for ALCHNM.

Let $X$ be a (smooth) compact complex surface. We show that the torsion subgroup of biholomorphic automorphism group $\operatorname{Aut}(X)$ is virtually nilpotent. Moreover, we study Tits alternative and virtual derived length solvable subgroups $\operatorname{Aut}(X)$.

In this paper, we introduce and characterize the concept of fuzzy almost generalized $e$-continuous mappings. Several interesting properties of these mappings are also given. Examples and counter examples are also given to illustrate the concepts introduced in the paper. We also introduce the concept of fuzzy $f T_{frac{1}{2}}e$-space, fuzzy $ge$-space, fuzzy regular $ge$-space and  fuzzy gener...

In this paper, we define a generalized Wielandt subgroup, local generalized Wielandt subgroup and its series for finite group and discuss its different basic properties which explain the notion of generalized Wielandt subgroup in a better way. We bound generalized Wielandt length as a function of nilpotency classes of its Sylow subgroups.

Fuzzy orderings with reference to an underlying context of similarity were first defined by Höhle and Blanchard [9]. Since then, several authors have contributed to the development of this class of fuzzy relations, both from the theoretical and the practical side (e.g. [1–4, 7, 8]). Two problems remained open throughout several years: how to define strict fuzzy orderings and how to define lexic...