نتایج جستجو برای: quasipermutable subgroup
تعداد نتایج: 85958 فیلتر نتایج به سال:
If N is a nontrivial proper normal subgroup of a finite group G then N and G/N are smaller than G. While it is false that G can be completely reconstructed from knowledge of N and G/N (see Example 1.1 below), it is nevertheless a standard technique in finite group theory to prove theorems about finite groups by induction on the size of the group and thereby use information about the smaller gro...
in this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite hamiltonian group. the coverings with three proper subgroups and the principal series of such a group are also counted. finally, we give a complete description of the lattice of characteristic subgroups of a finite h...
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.
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...
A theorem by Zacher and Rips states that the finiteness of the index of a subgroup can be described in terms of purely lattice-theoretic concepts. On the other hand, it is clear that if G is a group and H is a subgroup of finite index of G, the index |G : H| cannot be recognized in the lattice L(G) of all subgroups of G, as for instance all groups of prime order have isomorphic subgroup lattice...
In this paper, we deal with Molaei’s generalized groups. We definethe notion of a fuzzy generalized subgroup with respect to a t-norm (orT-fuzzy generalized subgroup) and give some related properties. Especially,we state and prove the Representation Theorem for these fuzzy generalizedsubgroups. Next, using the concept of continuity of t-norms we obtain a correspondencebetween TF(G), the set of ...
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