Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Publicado
On some invariants preserved by isomorphisms of tables of marks
Palabras clave:
Group representation, Burnside rings, table of marks (en)Representación de grupos, anillo de Burnside, tabla de marcas (es)
Descargas
Abstract. Let G and Q be groups with isomorphic tables of marks, and for each subgroup H of G, let H' denote a subgroup of Q assigned to H under an isomorphism between the tables of marks of G and Q. We prove that if H is cyclic/elementary abelian/maximal/the Frattini subgroup/the commutator subgroup, then H' has the same property. However, we give examples where H is abelian and H' is not, and where H is the centre of G and H' is not the centre of Q. For this we construct (using GAP) the smallest example of non-isomorphic groups with isomorphic tables of marks.
Referencias
R. Brandi and T. Huckle, On the isomorphism problem for Burnside rings, Proceedings of the American Mathematical Society 123 (1995), no. 12, 3623-3626.
The GAP Group, GAP - Groups, Algorithms and Programming, version 4-4, 2006, (http:www.gap-system.org).
W. Kimmerle, Beiträge zur ganzzahligen Darstellungstheorie endlicher Gruppen, vol. 36, Bayreuther Mathematische Schriften, 1991 (al).
W. Kimmerle, F. Luca, and A. Raggi-Cardenas, Irreducible components and isomophisms of the Burnside ring, Journal of Group Theory 11 (2008), no. 6, 831-844, DOI: 10.1515/JGT.2008.052.
W. Kimmerle and K. W. Roggenkamp, Automorphisms of Burnside rings, London Math. Soc. Lecture Note Ser. 212 (1995), 333-351.
F. Luca and A. Raggi-Cardenas, Composition factors from the table of marks, Journal of Algebra 244 (2001), 737-743.
A. Raggi-Cärdenas and L. Valero-Elizondo, Groups with isomorphic Biimside rings, Archiv der Mathematik 84 (2005), no. 3, 193-197, (31/Mar/2005). ISSN: 0003-889X. Publisher: Birkhäuser.
_____, Two non-isomorphic groups of order 96 with isomorphic tables of marks and non-corresponding centres and abelian subgroups, Communications in Algebra 37 (2009), 209-212, ISSN: 0092-7872, DOI: 10.1080/00927870802243614.
J. Thevenaz, Isomorphic Burnside rings, Communications in Algebra 16 (1988), no. 9, 1945-1947.
