Geodesic
Complex group algebras of finite groups: Brauer’s Problem 1
Moretó, Alexander1
1 Departament d’Àlgebra, Universitat de València, 46100 Burjassot, València, SPAIN
Electronic research announcements of the American Mathematical Society, Tome 11 (2005), pp. 34-39.

Voir la notice de l'article provenant de la source American Mathematical Society

Brauer’s Problem 1 asks the following: what are the possible complex group algebras of finite groups? It seems that with the present knowledge of representation theory it is not possible to settle this question. The goal of this paper is to announce a partial solution to this problem. We conjecture that if the complex group algebra of a finite group does not have more than a fixed number $m$ of isomorphic summands, then its dimension is bounded in terms of $m$. We prove that this is true for every finite group if it is true for the symmetric groups.
DOI : 10.1090/S1079-6762-05-00144-7

Moretó, Alexander 1

1 Departament d’Àlgebra, Universitat de València, 46100 Burjassot, València, SPAIN 
@article{ERAAMS_2005_11_a3,
     author = {Moret\'o, Alexander},
     title = {Complex group algebras of finite groups: {Brauer{\textquoteright}s} {Problem} 1},
     journal = {Electronic research announcements of the American Mathematical Society},
     pages = {34--39},
     publisher = {mathdoc},
     volume = {11},
     year = {2005},
     doi = {10.1090/S1079-6762-05-00144-7},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-05-00144-7/}
}
TY  - JOUR
AU  - Moretó, Alexander
TI  - Complex group algebras of finite groups: Brauer’s Problem 1
JO  - Electronic research announcements of the American Mathematical Society
PY  - 2005
SP  - 34
EP  - 39
VL  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-05-00144-7/
DO  - 10.1090/S1079-6762-05-00144-7
ID  - ERAAMS_2005_11_a3
ER  - 
%0 Journal Article
%A Moretó, Alexander
%T Complex group algebras of finite groups: Brauer’s Problem 1
%J Electronic research announcements of the American Mathematical Society
%D 2005
%P 34-39
%V 11
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-05-00144-7/
%R 10.1090/S1079-6762-05-00144-7
%F ERAAMS_2005_11_a3
Moretó, Alexander. Complex group algebras of finite groups: Brauer’s Problem 1. Electronic research announcements of the American Mathematical Society, Tome 11 (2005), pp. 34-39. doi : 10.1090/S1079-6762-05-00144-7. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-05-00144-7/

[1] Babai, László, Pyber, László Permutation groups without exponentially many orbits on the power set J. Combin. Theory Ser. A 1994 160 168

[2] Brauer, Richard Representations of finite groups 1963 133 175

[3] Erdős, Paul, Graham, S. W., Ivić, Aleksandar, Pomerance, Carl On the number of divisors of 𝑛! 1996 337 355

[4] Farias E Soares, Eliana Big primes and character values for solvable groups J. Algebra 1986 305 324

[5] Frame, J. S., Robinson, G. De B., Thrall, R. M. The hook graphs of the symmetric groups Canad. J. Math. 1954 316 324

[6] Hardy, G. H., Wright, E. M. An introduction to the theory of numbers 1979

[7] Huppert, Bertram Research in representation theory at Mainz (1984–1990) 1991 17 36

[8] Huppert, Bertram, Blackburn, Norman Finite groups. II 1982

[9] Isaacs, I. Martin Character theory of finite groups 1994

[10] Jaikin-Zapirain, A. On the number of conjugacy classes in finite 𝑝-groups J. London Math. Soc. (2) 2003 699 711

[11] Keller, Thomas Michael Orbits in finite group actions 2003 306 331

[12] Moretó, Alexander, Sangroniz, Josu On the number of conjugacy classes of zeros of characters Israel J. Math. 2004 163 187

Cité par Sources :