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A decomposition theory for finite groups with applications to P-groups

Citation

Weichsel, Paul M. (1960) A decomposition theory for finite groups with applications to P-groups. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-07072006-085918

Abstract

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Let [...] be a set of finite groups and define [...] to be the intersection of all sets of groups which contain [...] and are closed under the operations of subgroup, factor group and direct product. The equivalence relation defined by [...] if [...] = [...] is studied and it is shown that if Qn and Dn are the generalized quaternion group of order 2n and the dihedral group of order 2n then [...] = [...].

A group G is called decomposable if [...] with [...] the set of proper subgroups and factor groups of G. It is shown that if G is decomposable then G must contain a proper subgroup or factor group whose class is the same as the class of G and one whose derived length is the same as the derived length of G. The set of indecomposable p-groups of class two are characterized and for [...] their defining relations are compiled. It is also shown that if the exponent of G is p and the class of G is greater than two then G is decomposable if G/Z(G) is a direct product.

Finally the equivalence relation given above is modified and its connection with the isoclinism relation of P. Hall is investigated. It is shown that for a certain class of p-groups this relation is equivalent to isoclinism

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Dean, Richard A.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1960
Record Number:CaltechETD:etd-07072006-085918
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-07072006-085918
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2821
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:31 Jul 2006
Last Modified:26 Dec 2012 02:54

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