|
|
| |
| NON-ISOMORPHIC GROUPS WITH ISOMORPHIC SPECTRALTABLES AND BURNSIDE MATRICES |
| |
Citation： |
W. Kimmerle,K. W. Roggenkamp.NON-ISOMORPHIC GROUPS WITH ISOMORPHIC SPECTRALTABLES AND BURNSIDE MATRICES[J].Chinese Annals of Mathematics B,1994,15(3):273~282 |
| Page view： 1048
Net amount： 683 |
Authors： |
W. Kimmerle; K. W. Roggenkamp |
Foundation： |
This research was supported by the Deutsche Forschungsgemeinschaft |
|
|
| Abstract： |
It was shown by Formanek and Sibley that the group determinant
characterizes a finite group $G$ up to isomorphism. Hoehnke and
Johnson\,(independently the authors\,---\,using an argument of
Mansfield) showed the corresponding result for $k$-characters,
$k=1,2,3.$ The notion of $k$-characters dates back to Frobenius.
They are determined by the group determinant and may be derived
{from} the character table $CT(G)$ provided one knows additionally
the functions
$$\Phi_k: G\times\cdots \times G\to C(G),\ \ (g_1,\cdots, g_k)\to
C_{g_1\cdot\dots\cdot g_k},$$
where $C(G)=\{C_g,\ g\in G\}$ denotes the set of conjugacy
classes of $G$.
The object of the paper is to present criteria for finite groups
(more precisely for soluble groups $G$ and $H$ which are both
semi-direct products of a similar type) when
1. $G$ and $H$ have isomorphic spectral tables (i.e., they form a
Brauer pair),
2. $G$ and $H$ have isomorphic table of marks (in particular the
Burnside rings are isomorphic),
3. $G$ and $H$ have the same 2-characters.
Using this the authors construct two non-isomorphic soluble
groups for which all these three representation-theoretical
invariants coincide. |
Keywords： |
Finite group, Spectral table, Burnside matrix, Isomorphism. |
Classification： |
20C15, 20B25. |
|
|
Download PDF Full-Text
|
|
|
|
