Search results for "Quotient group"
showing 4 items of 4 documents
Topological Decompositions of the Pauli Group and their Influence on Dynamical Systems
2021
In the present paper we show that it is possible to obtain the well known Pauli group $P=\langle X,Y,Z \ | \ X^2=Y^2=Z^2=1, (YZ)^4=(ZX)^4=(XY)^4=1 \rangle $ of order $16$ as an appropriate quotient group of two distinct spaces of orbits of the three dimensional sphere $S^3$. The first of these spaces of orbits is realized via an action of the quaternion group $Q_8$ on $S^3$; the second one via an action of the cyclic group of order four $\mathbb{Z}(4)$ on $S^3$. We deduce a result of decomposition of $P$ of topological nature and then we find, in connection with the theory of pseudo-fermions, a possible physical interpretation of this decomposition.
Permutable products of supersoluble groups
2004
We investigate the structure of finite groups that are the mutually permutable product of two supersoluble groups. We show that the supersoluble residual is nilpotent and the Fitting quotient group is metabelian. These results are consequences of our main theorem, which states that such a product is supersoluble when the intersection of the two factors is core-free in the group.
Divisible designs and groups
1992
We study (s, k, λ1, λ2)-translation divisible designs with λ1≠0 in the singular and semi-regular case. Precisely, we describe singular (s, k, λ1, λ2)-TDD's by quasi-partitions of suitable quotient groups or subgroups of their translation groups. For semi-regular (s, k, λ1, λ2)-TDD's (and, more general, for the case λ2>λ1) we prove that their translation groups are either Frobenius groups or p-groups of exponent p. Some examples are given for the singular, semi-regular and regular case.
Anti-$PC$-groups and Anti-$CC$-groups
2007
A groupGhas Černikov classes of conjugate subgroups if the quotient groupG/coreG(NG(H))is a Černikov group for each subgroupHofG. An anti-CCgroupGis a group in which each nonfinitely generated subgroupKhas the quotient groupG/coreG(NG(K))which is a Černikov group. Analogously, a groupGhas polycyclic-by-finite classes of conjugate subgroups if the quotient groupG/coreG(NG(H))is a polycyclic-by-finite group for each subgroupHofG. An anti-PCgroupGis a group in which each nonfinitely generated subgroupKhas the quotient groupG/coreG(NG(K))which is a polycyclic-by-finite group. Anti-CCgroups and anti-PCgroups are the subject of the present article.