On the automorphism groups of rational group algebras of metacyclic groups

1997 ◽  
Vol 25 (7) ◽  
pp. 2085-2097 ◽  
Author(s):  
Allen Herman
Keyword(s):  
Automorphism Groups ◽  
Group Algebras ◽  
Rational Group ◽  
Metacyclic Groups

Units of Integral Group Rings of Some Metacyclic Groups

1994 ◽  
Vol 37 (2) ◽  
pp. 228-237 ◽  
Author(s):  
Eric Jespers ◽  
Guilherme Leal ◽  
C. Polcino Milies
Keyword(s):  
Finite Index ◽  
Unit Group ◽  
Group Algebras ◽  
Group Rings ◽  
Integral Group ◽  
Rational Group ◽  
Metacyclic Groups ◽  
Integral Group Rings ◽  
Almost All ◽  
Natural Way

AbstractIn this paper, we consider all metacyclic groups of the type 〈a,b | an - 1, b2 = 1, ba = aib〉 and give a concrete description of their rational group algebras. As a consequence we obtain, in a natural way, units which generate a subgroup of finite index in the full unit group, for almost all such groups.

Central Idempotents and Units in Rational Group Algebras of Alternating Groups

1998 ◽  
Vol 08 (04) ◽  
pp. 467-477 ◽  
Author(s):  
A. Giambruno ◽  
E. Jespers
Keyword(s):  
Group Algebra ◽  
Finite Index ◽  
Explicit Description ◽  
Alternating Group ◽  
Group Algebras ◽  
Young Tableaux ◽  
Rational Group ◽  
Alternating Groups ◽  
Group Of Units

Let ℚAn be the group algebra of the alternating group over the rationals. By exploiting the theory of Young tableaux, we give an explicit description of the minimal central idempotents of ℚAn. As an application we construct finitely many generators for a subgroup of finite index in the centre of the group of units of ℚAn.

Residual solvability of the unit groups of rational group algebras

1987 ◽  
Vol 48 (3) ◽  
pp. 213-216 ◽  
Author(s):  
Ashwani K. Bhandari ◽  
I. B. S. Passi
Keyword(s):  
Group Algebras ◽  
Rational Group

scholarly journals EXPLORATION OF FINITE-DIMENSIONAL KAC ALGEBRAS AND LATTICES OF INTERMEDIATE SUBFACTORS OF IRREDUCIBLE INCLUSIONS

2011 ◽  
Vol 10 (05) ◽  
pp. 995-1106 ◽  
Author(s):  
MARIE-CLAUDE DAVID ◽  
NICOLAS M. THIÉRY
Keyword(s):  
Automorphism Groups ◽  
Group Algebras ◽  
Self Duality ◽  
Finite Dimensional ◽  
Twisted Group ◽  
Galois Correspondence ◽  
Index 2 ◽  
Original Motivation ◽  
The Way

We study the four infinite families KA(n), KB(n), KD(n), and KQ(n) of finite-dimensional Hopf (in fact Kac) algebras constructed, respectively, by A. Masuoka and L. Vainerman: isomorphisms, automorphism groups, self-duality, lattices of coideal sub-algebras. We reduce the study to KD(n) by proving that the others are isomorphic to KD(n), its dual, or an index 2 subalgebra of KD(2n). We derive many examples of lattices of intermediate subfactors of the inclusions of depth 2 associated to those Kac algebras, as well as the corresponding principal graphs, which is the original motivation. Along the way, we extend some general results on the Galois correspondence for depth 2 inclusions, and develop some tools and algorithms for the study of twisted group algebras and their lattices of coideal subalgebras. This research was driven by heavy computer exploration, whose tools and methodology we describe.

scholarly journals Automorphisms of Cayley graphs of metacyclic groups of prime-power order

2001 ◽  
Vol 71 (2) ◽  
pp. 223-232 ◽  
Author(s):  
Caiheng Li ◽  
Hyo-Seob Sim
Keyword(s):  
Graph Theory ◽  
Cayley Graph ◽  
Prime Power ◽  
Automorphism Groups ◽  
Cayley Graphs ◽  
Prime Power Order ◽  
Subsequent Work ◽  
Metacyclic Groups

AbstractThis paper inverstigates the automorphism groups of Cayley graphs of metracyclicp-gorups. A characterization is given of the automorphism groups of Cayley grahs of a metacyclicp-group for odd primep. In particular, a complete determiniation of the automophism group of a connected Cayley graph with valency less than 2pof a nonabelian metacyclicp-group is obtained as a consequence. In subsequent work, the result of this paper has been applied to solve several problems in graph theory.

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