13,112 research outputs found
Primitive permutation groups and derangements of prime power order
Let be a transitive permutation group on a finite set of size at least
. By a well known theorem of Fein, Kantor and Schacher, contains a
derangement of prime power order. In this paper, we study the finite primitive
permutation groups with the extremal property that the order of every
derangement is an -power, for some fixed prime . First we show that these
groups are either almost simple or affine, and we determine all the almost
simple groups with this property. We also prove that an affine group has
this property if and only if every two-point stabilizer is an -group. Here
the structure of has been extensively studied in work of Guralnick and
Wiegand on the multiplicative structure of Galois field extensions, and in
later work of Fleischmann, Lempken and Tiep on -semiregular pairs.Comment: 30 pages; to appear in Manuscripta Mat
Derangements in primitive permutation groups, with an application to character theory
Let be a finite primitive permutation group and let be the
number of conjugacy classes of derangements in . By a classical theorem of
Jordan, . In this paper we classify the groups with
, and we use this to obtain new results on the structure of finite
groups with an irreducible complex character that vanishes on a unique
conjugacy class. We also obtain detailed structural information on the groups
with , including a complete classification for almost simple
groups.Comment: 29 page
A Model of Quark and Lepton Masses I: The Neutrino Sector
If neutrinos have masses, why are they so tiny? Are these masses of the Dirac
type or of the Majorana type? We are already familiar with the mechanism of how
to obtain a tiny Majorana neutrino mass by the famous see-saw mechanism. The
question is: Can one build a model in which a tiny Dirac neutrino mass arises
in a more or less "natural" way? What would be the phenomenological
consequences of such a scenario, other than just merely reproducing the
neutrino mass patterns for the oscillation data? In this article, a systematic
and detailed analysis of a model is presented, with, as key components, the
introduction of a family symmetry as well as a new SU(2) symmetry for the
right-handed neutrinos. In particular, in addition to the calculations of light
neutrino Dirac masses, interesting phenomenological implications of the model
will be presented.Comment: 25 (single-spaced) pages, 11 figures, corrected some typos in Table
I, added acknowledgement
Approximate gauge symmetry of composite vector bosons
It can be shown in a solvable field theory model that the couplings of the
composite vector bosons made of a fermion pair approach the gauge couplings in
the limit of strong binding. Although this phenomenon may appear accidental and
special to the vector boson made of a fermion pair, we extend it to the case of
bosons being constituents and find that the same phenomenon occurs in more an
intriguing way. The functional formalism not only facilitates computation but
also provides us with a better insight into the generating mechanism of
approximate gauge symmetry, in particular, how the strong binding and global
current conservation conspire to generate such an approximate symmetry. Remarks
are made on its possible relevance or irrelevance to electroweak and higher
symmetries.Comment: Correction of typos. The published versio
Interacting Business Cycle Fluctuations: A Two-Country Model
In this paper, we develop a model of business cycle fluctuations between two interacting open economies within the disequilibrium or non-market clearing paradigm. We analyze the main feedback mechanisms (Keynes, Mundell, Rose and Dornbusch) driving the dynamics and the conflict between their stabilizing and destabilizing tendencies and how these depend on certain key speeds of adjustment in the real and foreign exchange sectors. We explore numerically a variety of situations of interacting price cycles in the two countries, where the steady state is locally repelling, but where the overall dynamics are bounded in an economically meaningful domain by assuming downward money wage rigidity
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