Vol. 15, No. 4, 1965

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The 2-length of a finite solvable group

Fletcher Gross

Vol. 15 (1965), No. 4, 1221–1237

One measure of the structure of a finite solvable group G is its p-length lp(G). A problem connected with this measure is to obtain an upper bound for lp(G) in terms of ep(G), which is a numerical invariant of the Sylow p-subgroups of G. This problem has been solved but the best-possible result is not known for p = 2. The main result of this paper is that l2(G) 2e2(G) 1, which is an improvement on earlier results. A secondary objective of this paper is to investigate finite solvable groups in which the Sylow 2-group is of exponent 4. In particular it is proved that if G is a finite group of exponent 12, then the 2-length is at most 2.

Mathematical Subject Classification
Primary: 20.40
Received: 13 July 1964
Published: 1 December 1965
Fletcher Gross