Citation
Weichsel, Paul M. (1960) A decomposition theory for finite groups with applications to Pgroups. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/FCJW5875. https://resolver.caltech.edu/CaltechETD:etd07072006085918
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 pgroups 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 pgroups 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): 

Thesis Committee: 

Defense Date:  1 January 1960 
Record Number:  CaltechETD:etd07072006085918 
Persistent URL:  https://resolver.caltech.edu/CaltechETD:etd07072006085918 
DOI:  10.7907/FCJW5875 
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 ETDdb 
Deposited On:  31 Jul 2006 
Last Modified:  21 Dec 2019 01:48 
Thesis Files

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