let $h$, $l$ and $x$ be subgroups of a finite group$g$. then $h$ is said to be $x$-permutable with $l$ if for some$xin x$ we have $al^{x}=l^{x}a$. we say that $h$ is emph{$x$-quasipermutable } (emph{$x_{s}$-quasipermutable}, respectively) in $g$ provided $g$ has a subgroup$b$ such that $g=n_{g}(h)b$ and $h$ $x$-permutes with $b$ and with all subgroups (with all sylowsubgroups, respectively) $v$...

The orientation preserving topological symmetry group of a graph embedded in the 3-sphere is the subgroup of the automorphism group of the graph consisting of those automorphisms which can be induced by an orientation preserving homeomorphism of the ambient space. We characterize all possible orientation preserving topological symmetry groups of embeddings of complete graphs in the 3-sphere.

Let p ≥ 5 be a prime number. We prove that the abstract commensurator of the Nottingham group N (Fp) coincides with its automorphism group, which is known to be a finite extension of N (Fp). As a corollary we deduce that the Nottingham group cannot be embedded as an open subgroup of a topologically simple group.

Let U be a unital embedded in the Desarguesian projective plane PG(2, q 2). Write M for the subgroup of PGL(3, q 2) which preserves U. We show that U is classical if and only if U has two distinct points P, Q for which the stabiliser G = MP,Q has order q 2 − 1.

We construct an embedding of any right-angled Artin group into a graph braid group. We include an observation which decreases the number of strands of the graph braid group required for this embedding, yielding an example of a hyperbolic surface subgroup embedded in a two strand planar graph braid group.

We study the rigidity of complete, embedded constant mean curvature surfaces in R 3 . Among other things, we prove that when such a surface has finite genus, then intrinsic isometries of the surface extend to isometries of R 3 or its isometry group contains an index two subgroup of isometries that extend. Mathematics Subject Classification: Primary 53A10, Secondary 49Q05, 53C42

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

There are various types of classifiers that can be trained on gene expression data with class labels. Many of them have an embedded mechanism for feature selection, by which they distinguish a subset of significant genes that are used for future prediction. When dealing with more than two class labels, especially when the number goes up to a dozen or more, people find it useful to know the rela...

This paper presents a semi-automatic approach for confounding-aware subgroup discovery: Confounding essentially disturbs the measured effect of an association between variables due to the influence of other parameters that were not considered. The proposed method is embedded into a general subgroup discovery approach, and provides the means for detecting potentially confounded subgroup patterns...

There is a longstanding conjecture, due to Gregory Cherlin and Boris Zilber, that all simple groups of finite Morley rank are simple algebraic groups. One of the major theorems in the area is Borovik’s trichotomy theorem. The ‘trichotomy’ here is a case division of the generic minimal counterexamples within odd type, that is, groups with a large and divisible Sylow◦ 2-subgroup. The so-called ‘u...