The classification of finite p-groups up to isomorphism is an
intricate problem in group theory. In particular, a classification
by order seems to be hopeless in general. In 1980, Leedham-Green
and Newman suggested to classify p-groups by coclass. This has led
to a new research area which delivered a deep insight into the
structure of p-groups. New approaches and results concerning a
classification by coclass have been developed since 1999, and it is
known that the 2-groups of fixed coclass can be classified. A
fundamental tool in this approach is the investigation of the
coclass graph associated with these groups. For odd primes, a
similar classification is still open. As an important special case,
the author Heiko Dietrich investigates the p-groups of coclass 1,
that is, the p-groups of maximal class. These are the p-groups of
order p to the power of n with nilpotency class n-1. He gives a
survey on the known structure of these groups and he proved two
types of periodic patterns in the associated coclass graph. These
patterns are reflected in the structure of the groups and the
achieved results strongly support the conjecture that the p-groups
of maximal class can be classified.
General
Imprint: |
Sudwestdeutscher Verlag Fur Hochschulschriften AG
|
Country of origin: |
United States |
Release date: |
August 2009 |
First published: |
August 2009 |
Authors: |
Heiko Dietrich
|
Dimensions: |
229 x 152 x 7mm (L x W x T) |
Format: |
Paperback - Trade
|
Pages: |
132 |
ISBN-13: |
978-3-8381-1005-9 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
General
|
LSN: |
3-8381-1005-6 |
Barcode: |
9783838110059 |
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