The minimal faithful degree of a semilattice of groups

AbstractThis paper constructs a minimal faithful representation of a semilattice of groups by partial transformations. The solution is expressed in terms of join irreducible elements of the semilattice and minimal faithful representations of groups with respect to certain normal subgroups.

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On faithful quasi-permutation representations of groups of order p5

Journal of Algebra and Its Applications ◽

10.1142/s021949881850127x ◽

2018 ◽

Vol 17 (07) ◽

pp. 1850127

Author(s):

H. Behravesh ◽

M. Delfani

Keyword(s):

Finite Group ◽

Minimal Degree ◽

Faithful Representation ◽

Complex Field ◽

Rational Field ◽

Representations Of Groups ◽

Permutation Matrices ◽

A Finite Group

For a finite group [Formula: see text], we denote by [Formula: see text] the minimal degree of faithful permutation representations of [Formula: see text], and denote by [Formula: see text] and [Formula: see text], the minimal degree of faithful representation of [Formula: see text] by quasi-permutation matrices over the rational field [Formula: see text] and the complex field [Formula: see text], respectively. In this paper, we calculate [Formula: see text], [Formula: see text] and [Formula: see text] for the groups of order [Formula: see text], where [Formula: see text] is an odd prime.

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Cocycles and representations of groups of CAR type

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

10.1017/s1446788700026471 ◽

1986 ◽

Vol 40 (1) ◽

pp. 20-33 ◽

Cited By ~ 2

Author(s):

A. L. Carey ◽

William Moran

Keyword(s):

Normal Subgroup ◽

Representation Theory ◽

Irreducible Representations ◽

Normal Subgroups ◽

Systematic Account ◽

Representations Of Groups ◽

Twisted Group

AbstractRepresentations of non-type I groups G which may be expressed as an increasing union of type I normal subgroups are considered. Groups with this structure are natural generalisations of the CAR algebra (viewed as a twisted group C*-algebra) and are also group theoretic analogues of AF algebras. This paper gives a systematic account of their representation theory based on a canonical construction of one-cocycles for the G-action on the dual of a normal subgroup. Some examples are considered showing how to construct inquivalent irreducible representations (non-cohomologous cocycles) and also factor representations by a method which generalises the well-known construction of non-isomorphic factors for the CAR algebra.

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A note on the normal subgroups of mapping class groups

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100063957 ◽

1986 ◽

Vol 99 (1) ◽

pp. 79-87 ◽

Cited By ~ 16

Author(s):

D. D. Long

Keyword(s):

Mapping Class Group ◽

Class Group ◽

Mapping Class Groups ◽

Orientable Surface ◽

Faithful Representation ◽

Mapping Class ◽

Normal Subgroups ◽

Class Groups ◽

Closed Orientable Surface

0. If Fg is a closed, orientable surface of genus g, then the mapping class group of Fg is the group whose elements are orientation preserving self homeomorphisms of Fg modulo isotopy. We shall denote this group by Mg. Recall that a group is said to be linear if it admits a faithful representation as a group of matrices (where the entries for this purpose will be in some field).

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Vérités et Mensonges

Classical Antiquity ◽

10.1525/ca.2020.39.2.188 ◽

2020 ◽

Vol 39 (2) ◽

pp. 188-224

Author(s):

Erik Gunderson

Keyword(s):

Theory And Practice ◽

The Self ◽

Faithful Representation ◽

Political Subject ◽

Concrete Reality ◽

Hermeneutic Process ◽

The Way

This is a survey of some of the problems surrounding imperial panegyric. It includes discussions of both the theory and practice of imperial praise. The evidence is derived from readings of Cicero, Quintilian, Pliny, the Panegyrici Latini, Menander Rhetor, and Julian the Apostate. Of particular interest is insincere speech that would be appreciated as insincere. What sort of hermeneutic process is best suited to texts that are politically consequential and yet relatively disconnected from any obligation to offer a faithful representation of concrete reality? We first look at epideictic as a genre. The next topic is imperial praise and its situation “beyond belief” as well as the self-positioning of a political subject who delivers such praise. This leads to a meditation on the exculpatory fictions that these speakers might tell themselves about their act. A cynical philosophy of Caesarism, its arbitrariness, and its constructedness abets these fictions. Julian the Apostate receives the most attention: he wrote about Caesars, he delivered extant panegyrics, and he is also the man addressed by still another panegyric. And in the end we find ourselves to be in a position to appreciate the way that power feeds off of insincerity and grows stronger in its presence.

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On F-Normal Subgroups of Finite Soluble Groups

Journal of Algebra ◽

10.1006/jabr.1995.1008 ◽

1995 ◽

Vol 171 (1) ◽

pp. 189-203 ◽

Cited By ~ 4

Author(s):

A. Ballesterbolinches ◽

K. Doerk ◽

M.D. Perezramos

Keyword(s):

Normal Subgroups ◽

Soluble Groups

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On finite degree partial representations of groups

Journal of Algebra ◽

10.1016/s0021-8693(03)00533-7 ◽

2004 ◽

Vol 274 (1) ◽

pp. 309-334 ◽

Cited By ~ 11

Author(s):

M. Dokuchaev ◽

N. Zhukavets

Keyword(s):

Finite Degree ◽

Representations Of Groups

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Normal subgroups of diffeomorphism and homeomorphism groups of ℝn and other open manifolds

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385710000659 ◽

2011 ◽

Vol 31 (6) ◽

pp. 1835-1847 ◽

Cited By ~ 1

Author(s):

PAUL A. SCHWEITZER, S. J.

Keyword(s):

Normal Subgroup ◽

Compact Manifold ◽

Normal Subgroups ◽

Open Manifold ◽

Open Manifolds ◽

Group Of Homeomorphisms ◽

Homeomorphism Groups

AbstractWe determine all the normal subgroups of the group of Cr diffeomorphisms of ℝn, 1≤r≤∞, except when r=n+1 or n=4, and also of the group of homeomorphisms of ℝn ( r=0). We also study the group A0 of diffeomorphisms of an open manifold M that are isotopic to the identity. If M is the interior of a compact manifold with non-empty boundary, then the quotient of A0 by the normal subgroup of diffeomorphisms that coincide with the identity near to a given end e of M is simple.

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Polygonal products of polycyclic by finite groups

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700021778 ◽

1996 ◽

Vol 54 (3) ◽

pp. 369-372 ◽

Cited By ~ 4

Author(s):

R.B.J.T. Allenby

Keyword(s):

Finite Groups ◽

Cyclic Subgroup ◽

Substantial Improvement ◽

Normal Subgroups ◽

Recent Theorem

We prove that a polygonal product of polycyclic by finite groups amalgamating normal subgroups, with trivial mutual intersections, is cyclic subgroup separable. Because of a recent example (stated below) of the author this substantial improvement on a recent theorem of Kim is essentially best possible.

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