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Group algebra series and coboundary modules
The shift action on the 2-cocycle group Z 2 ( G , C ) of a finite group G with coefficients in a finitely generated abelian group C has several useful applications in combinatorics and digital communications, arising from the invariance of a uniform distribution property of cocycles under the action...
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| Published in: | Journal of pure and applied algebra 2010-07, Vol.214 (7), p.1291-1300 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | The
shift action on the 2-cocycle group
Z
2
(
G
,
C
)
of a finite group
G
with coefficients in a finitely generated abelian group
C
has several useful applications in combinatorics and digital communications, arising from the invariance of a uniform distribution property of cocycles under the action. In this article, we study the shift orbit structure of the coboundary subgroup
B
2
(
G
,
C
)
of
Z
2
(
G
,
C
)
. The study is placed within a well-known setting involving the Loewy and socle series of a group algebra over
G
. We prove new bounds on the dimensions of terms in such series. Asymptotic results on the size of shift orbits are also derived; for example, if
C
is an elementary abelian
p
-group, then almost all shift orbits in
B
2
(
G
,
C
)
are maximal-sized for large enough finite
p
-groups
G
of certain classes. |
|---|---|
| ISSN: | 0022-4049 1873-1376 |
| DOI: | 10.1016/j.jpaa.2009.10.016 |