The 2-groups of coclass 1 are widely known and James (in 1975) looked at the 2-groups of coclass 2. Development of the p-group generation algorithm implemented by O'Brien at ANU enabled group presentations to be provided for the 2-groups of coclass 3 by Newman and O'Brien for groups of order up to 223. Newman and O'Brien (in 1999) conjectured the number of descendants of 2n for all n. They introduced the concept of a family, with each family related to a different pro-p-group and the concept of a sporadic p-group, a p-group external to any family. They found 1782 sporadic 2-groups with order at most 214. The 70 families of 2-groups of coclass 3 can be further split according to their period, a measure of the repetitive structure of the families. Newman and O'Brien conjectured that these families had periods of 1, 2 or 4. This thesis examines the 2-groups of coclass 3 contained in families with period 1 and shows that the number of descendants conjectured by Newman and O'Brien is correct. Furthermore the presentation of all groups contained in period 1 families is provided and shown to be correct.
| Identifer | oai:union.ndltd.org:ADTP/187000 |
| Date | January 2000 |
| Creators | Smith, Duncan Alexander, Mathematics, UNSW |
| Publisher | Awarded by:University of New South Wales. Mathematics |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | Copyright Duncan Alexander Smith, http://unsworks.unsw.edu.au/copyright |
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