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The Derived Series of a p-Group


Hobby, Charles Ray (1960) The Derived Series of a p-Group. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/QY7G-Q706.


NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. 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.))
Subject Keywords:(Mathematics)
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 (advisor)
  • Zassenhaus, Hans (advisor)
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1960
Record Number:CaltechETD:etd-06152006-083527
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2608
Deposited By: Imported from ETD-db
Deposited On:23 Jun 2006
Last Modified:07 Nov 2023 18:04

Thesis Files

PDF (Hobby_c_1960.pdf) - Final Version
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