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Type of Document	Dissertation
Author	Gross, Fletcher
URN	etd-09192002-161906
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-09192002-161906
Title	The 2-length of a finite solvable group
Degree	PhD
Option	Mathematics
Advisory Committee	Advisor Name Title Marshall Hall Committee Chair
Keywords	None
Date of Defense	1964-01-01
Availability	unrestricted
Abstract NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. In this paper the relationship between the 2-length [...] and the 2-exponent [...] of a finite solvable group G is studied. It is shown that [...] - 1 provided that [...]. The special case of groups satisfying [...] = 2, i.e., groups whose Sylow 2-groups are of exponent 4, is investigated to determine whether [...] in this case. This question is not answered but it is shown that a certain normal subgroup (which may be the whole group) satisfies [...]. In addition if all the elements of order 4 are contained in this subgroup, then [...] for the whole group as well. As an application of this last result, it is proved that [...] in a group of exponent 12
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    Gross_f_1964.pdf 1.77 Mb 00:08:11 00:04:12 00:03:41 00:01:50 00:00:09