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The derived series of a p-group

Citation

Hobby, Charles Ray (1960) The derived series of a p-group. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-06152006-083527

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 p-groups 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 non-cyclic abelian p-group. 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 non-abelian p-group 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):
  • Taussky-Todd, Olga
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1960
Record Number:CaltechETD:etd-06152006-083527
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-06152006-083527
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 ETD-db
Deposited On:23 Jun 2006
Last Modified:26 Dec 2012 02:53

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