Citation
Hobby, Charles Ray (1960) The derived series of a pgroup. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd06152006083527
Abstract
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Olga Taussky (see W. Magnus, Math. Ann. vol. 111 (1935)) posed the problem of determining whether there is an infinite chain of pgroups G1, G2,..., such that G1 is abelian, [...], and [...] where [...] is the nth derived group of [...]. N. Ito (Nagoya Math. J., vol. 1, (1950)) constructed such a chain for p > 2 and G1 of type (p,p,p). It is shown (by an explicit construction) that if p > 2 there is a chain of the required kind for G1 any noncyclic abelian pgroup. If p = 2 there is a chain of the required kind if G1 contains a subgroup of type [...], of type [...], of type [...], or of type (2,2,2,2,2). As a consequence, for p > 2 it is impossible to estimate the length of the derived series of a nonabelian pgroup G from the type of [...]. This gives a negative answer (for p > 2) to a question posed by O. Taussky (Research Problem 9, Bull. Amer. Math. Soc. vol. 64 (1958) pp. 124).
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:etd06152006083527 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd06152006083527 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  2608 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  23 Jun 2006 
Last Modified:  26 Dec 2012 02:53 
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