Search results for "Permutation group"
showing 10 items of 46 documents
Magic informationally complete POVMs with permutations
2017
Eigenstates of permutation gates are either stabilizer states (for gates in the Pauli group) or magic states, thus allowing universal quantum computation [M. Planat and Rukhsan-Ul-Haq, Preprint 1701.06443]. We show in this paper that a subset of such magic states, when acting on the generalized Pauli group, define (asymmetric) informationally complete POVMs. Such IC-POVMs, investigated in dimensions $2$ to $12$, exhibit simple finite geometries in their projector products and, for dimensions $4$ and $8$ and $9$, relate to two-qubit, three-qubit and two-qutrit contextuality.
Efficacy and complications associated with a modified inferior alveolar nerve block technique. A randomized, triple-blind clinical trial
2014
Objectives: To compare the efficacy and complication rates of two different techniques for inferior alveolar nerve blocks (IANB). Study Design: A randomized, triple-blind clinical trial comprising 109 patients who required lower third molar removal was performed. In the control group, all patients received an IANB using the conventional Halsted technique, whereas in the experimental group, a modified technique using a more inferior injection point was performed. Results: A total of 100 patients were randomized. The modified technique group showed a significantly higher onset time in the lower lip and chin area, and was frequently associated to a lingual electric discharge sensation. Three f…
Multiply Transitive Permutation Groups
1982
Since the beginnings of finite group theory, the multiply transitive permutation groups have exercised a certain fascination. This is mainly due to the fact that apart from the symmetric and alternating groups not many of them were known. Only very recently final results about multiply transitive permutation groups have been proved, using the classification of all finite simple groups (see 7.5).
A class of imprimitive groups
2010
We classify imprimitive groups inducing the alternating group A4 on the set of blocks, with the inertia subgroup satisfying some very natural geometrical conditions which force the group to operate linearly.
Some contributions to the theory of transformation monoids
2019
The aim of this paper is to present some contributions to the theory of finite transformation monoids. The dominating influence that permutation groups have on transformation monoids is used to describe and characterise transitive transformation monoids and primitive transitive transformation monoids. We develop a theory that not only includes the analogs of several important theorems of the classical theory of permutation groups but also contains substantial information about the algebraic structure of the transformation monoids. Open questions naturally arising from the substantial paper of Steinberg [A theory of transformation monoids: combinatorics and representation theory. Electron. J…
HEIGHTS OF CHARACTERS IN BLOCKS OF $p$-SOLVABLE GROUPS
2005
In this paper, it is proved that if $B$ is a Brauer $p$ -block of a $p$ -solvable group, for some odd prime $p$ , then the height of any ordinary character in $B$ is at most $2b$ , where $p^b$ is the largest degree of the irreducible characters of the defect group of $B$ . Some other results that relate the heights of characters with properties of the defect group are obtained.
Central Units, Class Sums and Characters of the Symmetric Group
2010
In the search for central units of a group algebra, we look at the class sums of the group algebra of the symmetric group S n in characteristic zero, and we show that they are units in very special instances.
Group algebras whose units satisfy a group identity
1997
Let F G FG be the group algebra of a torsion group over an infinite field F F . Let U U be the group of units of F G FG . We prove that if U U satisfies a group identity, then F G FG satisfies a polynomial identity. This confirms a conjecture of Brian Hartley.
The complex of words and Nakaoka stability
2005
We give a new simple proof of the exactness of the complex of injective words and use it to prove Nakaoka's homology stability for symmetric groups. The methods are generalized to show acyclicity in low degrees for the complex of words in "general position". Hm(§ni1;Z) = Hm(§n;Z) for n=2 > m where §n denotes the permutation group of n elements. An elementary proof of this fact has not been available in the literature. In the first section the complex C⁄(m) of abelian groups is studied which in de- gree n is freely generated by injective words of length n. The alphabet consists of m letters. The complex C⁄(m) has the only non vanishing homology in degree m (Theorem 1). This is a result of F.…
Asymptotics for the standard and the Capelli identities
2003
Let {c n (St k )} and {c n (C k )} be the sequences of codimensions of the T-ideals generated by the standard polynomial of degreek and by thek-th Capelli polynomial, respectively. We study the asymptotic behaviour of these two sequences over a fieldF of characteristic zero. For the standard polynomial, among other results, we show that the following asymptotic equalities hold: $$\begin{gathered} c_n \left( {St_{2k} } \right) \simeq c_n \left( {C_{k^2 + 1} } \right) \simeq c_n \left( {M_k \left( F \right)} \right), \hfill \\ c_n \left( {St_{2k + 1} } \right) \simeq c_n \left( {M_{k \times 2k} \left( F \right) \oplus M_{2k \times k} \left( F \right)} \right), \hfill \\ \end{gathered} $$ wher…