a normal subgroup $n$ of a group $g$ is said to be an‎ ‎$emph{omissible}$ subgroup of $g$ if it has the following property‎: ‎whenever $xleq g$ is such that $g=xn$‎, ‎then $g=x$‎. ‎in this note we construct various groups $g$‎, ‎each of which has an omissible subgroup $nneq 1$ such that $g/ncong sl_2(k)$ where $k$ is a field of positive characteristic‎.

a group $g$ is called metahamiltonian if all its non-abelian subgroups are normal‎. ‎the aim of this paper is to provide an updated survey of research concerning certain classes of generalized metahamiltonian groups‎, ‎in various contexts‎, ‎and to prove some new results‎. ‎some open problems are listed‎.

SO(3) it is the proper symmetry group of the icosahedron (and the dodecahedron). It is the unique finite subgroup of SO(3) which equals its own commutator subgroup—in fact, it is the unique non-abelian simple finite subgroup of SO(3). It can be thought of as the beginning or smallest member of the family of non-abelian finite simple groups. From the point of view of the McKay correspondence it ...

Motivated by cryptography, permutations induced by polynomial functions on finite lattices L = (L,∨,∧,∗ ) with an antitone involution ∗ are investigated. These permutations together with the operation of composition form a subgroup of the symmetric group on L. We describe the structure of this subgroup for different classes of lattices L and indicate possible applications by outlining a protoco...

an algebraic construction for constant dimension subspace codes is called orbit code. it arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. in particular orbit codes of a singer subgroup of the general linear group has investigated recently. in this paper, we consider the normalizer of a singer subgroup of the general linear group a...

Clarifying the spatial correlation network structure of green development efficiency (GDE) is great significance for realizing coordinated and sustainable in China. By constructing evaluation index system GDE, this study used super epsilon-based measure (EBM) model that considers undesirable output to GDE China from 2000 2018, based on which characteristics influencing factors were analyzed usi...

The Hawaiian Drosophilidae contains approximately 1000 species, placed in species groups and subgroups based largely on secondary sexual modifications to wings, forelegs and mouthparts. Members of the spoon tarsus subgroup possess a cup-shaped structure on the foretarsi of males. Eight of the twelve species in this subgroup are found only on the Big Island of Hawaii, suggesting that they have d...

Abundant content, data type and diverse members’ interests naturally lead to preference heterogeneity within a multicast session requiring frequent communication within subgroups of members sharing common interests/requirements. In this paper, we propose a topology-sensitive subgroup communication (TSC) mechanism to support efficient subgroup communications in large-scale multicast applications...

In the paper, we consider a preference heterogeneity problem in large-scale multicast applications. Abundant content, data type and diverse members’ interests naturally lead to preference heterogeneity within a multicast session requiring frequent communication within subgroups of members sharing common interests/requirements. In this paper, we take an overlay approach which builds topology-sen...

‎let $g$ be a finite $p$-group and $n$ be a normal subgroup of $g$ with‎ ‎$|n|=p^n$ and $|g/n|=p^m$‎. ‎a result of ellis (1998) shows‎ ‎that the order of the schur multiplier of such a pair $(g,n)$ of finite $p$-groups is bounded‎ ‎by $ p^{frac{1}{2}n(2m+n-1)}$ and hence it is equal to $‎ ‎p^{frac{1}{2}n(2m+n-1)-t}$ for some non-negative integer $t$‎. ‎recently‎, ‎the authors have characterized...