Search results for "Quaternion"

Area minimizing projective planes on the projective space of dimension 3 with the Berger metric

2016

Abstract We show that, among the projective planes embedded into the real projective space R P 3 endowed with the Berger metric, those of least area are exactly the ones obtained by projection of the equatorial spheres of S 3 . This result generalizes a classical result for the projective spaces with the standard metric.

ZEROS OF CHARACTERS ON PRIME ORDER ELEMENTS

2001

Suppose that G is a finite group, let χ be a faithful irreducible character of degree a power of p and let P be a Sylow p-subgroup of G. If χ(x) ≠ 0 for all elements of G of order p, then P is cyclic or generalized quaternion. * The research of the first author is supported by a grant of the Basque Government and by the University of the Basque Country UPV 127.310-EB160/98. † The second author is supported by DGICYT.

Transitive factorizations in the hyperoctahedral group

2008

The classical Hurwitz enumeration problem has a presentation in terms of transitive factor- izationsin the symmetric group. This presentationsuggestsageneralizationfromtypeAto otherfinite reflection groups and, in particular, to type B.W e study this generalization both from ac ombinatorial and a geometric point of view, with the prospect of providing am eans of understanding more of the structure of the moduli spaces of maps with an S2-symmetry. The type A case has been well studied and connects Hurwitz numbers to the moduli space of curves. W ec onjecture an analogous setting for the type B case that is studied here. 1I ntroduction Transitive factorizations of permutations into transposit…

Two groups with isomorphic group algebras

1990

Partial spreads in finite projective spaces and partial designs

1975

A partial t-spread of a projective space P is a collection 5 p of t-dimensional subspaces of P of the same order with the property that any point of P is contained in at most one element of 50. A partial t-spread 5 p of P is said to be a t-spread if each point of P is contained in an element of 5P; a partial t-spread which is not a spread will be called strictly partial. Partial t-spreads are frequently used for constructions of affine planes, nets, and Sperner spaces (see for instance Bruck and Bose [5], Barlotti and Cofman [2]). The extension of nets to affine planes is related to the following problem: When can a partial t-spread 5 ~ of a projective space P be embedded into a larger part…

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.

Divisible Designs Admitting, as an Automorphism Group, an Orthogonal Group or a Unitary Group

2001

We construct some divisible designs starting from a projective space. These divisible designs admit an orthogonal group or a unitary group as an automorphism group.

2-Groups with few rational conjugacy classes

2011

Abstract In this paper we prove the following conjecture of G. Navarro: if G is a finite 2-group with exactly 5 rational conjugacy classes, then G is dihedral, semidihedral or generalized quaternion. We also characterize the 2-groups with 4 rational classes.

On t-covers in finite projective spaces

1979

A t-cover of the finite projective space PG(d,q) is a setS of t-dimensional subspaces such that any point of PG(d,q) is contained in at least one element ofS. In Theorem 1 a lower bound for the cardinality of a t-coverS in PG(d,q) is obtained and in Theorem 2 it is shown that this bound is best possible for all positive integers t,d and for any prime-power q.