in this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.

a subgroup x of a group g is said to be an h -subgroup if n_g(x) ∩ x^g ≤ x for each element g belonging to g. in [m. bianchi e. a., on finite soluble groups in which normality is a transitive relation, j. group theory, 3 (2000), 147–156] the authors showed that finite groups in which every subgroup has the h -property are exactly soluble groups in which normality is a transitive relation. here ...

Sufficient conditions are given for groups of finite Morley rank having non-trivial torsion-free nilpotent normal subgroups to have linear representations with small kernels. In particular, centreless connected soluble groups of finite Morley rank with torsion-free Fitting subgroups have faithful linear representations. On the way, using a notion of definable weight space, we prove that certain...

If a class of nitely generated groups G is closed under isometric amalgamations along free subgroups, then every G 2 G can be quasi-isometrically embedded in a group Ĝ 2 G that has no proper subgroups of nite index. Every compact, connected, non-positively curved space X admits an isometric embedding into a compact, connected, non-positively curved space X such that X has no non-trivial nite-sh...

If a class of finitely generated groups G is closed under isometric amalgamations along free subgroups, then every G ∈ G can be quasi-isometrically embedded in a group Ĝ ∈ G that has no proper subgroups of finite index. Every compact, connected, non-positively curved space X admits an isometric embedding into a compact, connected, non-positively curved space X such that X has no non-trivial fin...

1. Morley, Marsh, Baldwin/Lachlan, Zilber; and Macintyre 2 2. The Borovik Program: CFSG and tameness 3 2.1. The setting: tame or not 3 2.2. The basic framework: even, odd, mixed, degenerate 4 3. Mixed type 5 3.1. Strong and weak embedding 5 3.2. Toward weak embedding: U(G) 6 3.3. The subgroups B(G) and D(G) 6 3.4. The strategy 7 3.5. The curious incident of the dog in the night 8 3.6. Weak embe...

We show that many 3-manifold groups have no nonabelian surface subgroups. For example, any link of an isolated complex surface singularity has this property. In fact, we determine the exact class of closed graph-manifolds which have no immersed 1 -injective surface of negative Euler characteristic. We also determine the class of closed graph manifolds which have no nite cover containing an embe...

We study Morse subgroups and boundaries of random right-angled Coxeter groups in the Erdős–Rényi model. show that at densities below $$\left( \sqrt{\frac{1}{2}}-\epsilon \right) \sqrt{\frac{\log {n}}{n}}$$ almost surely have hyperbolic surface subgroups. This implies their contain embedded circles. Further, above \sqrt{\frac{1}{2}}+\epsilon we that, surely, special a group are virtually free. a...

a novel zinc oxide - agar nanocomposite was successfully synthesized using zinc chloride as a precursor. the nanocomposite was prepared using a domestic microwave oven. the prepared nanocomposites have been characterized by fourier transform infrared (ftir) spectroscopy, x-ray diffraction (xrd) analysis, scanning electron microscopy (sem) and uv- visible spectroscopy. the crystalline properties...

in this paper, we introduce some properties of an intuitionistic normal fuzzy m-subgroup of m- group with m-homomorphism and isomorphism. we study he image, the pre-image and the inverse mapping of the intuitionistic normal fuzzy m-‎subgroups.‎