Vol. 45, No. 2, 1973

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Generalized Sylow tower groups. II

James B. Derr and N. P. Mukherjee

Vol. 45 (1973), No. 2, 427–434

A well-known result of P. Hall shows that finite solvable groups may be characterized by a permutability requirement on Sylow subgroups. The notion of a generalized Sylow tower group (GSTG) arises when this permutability condition on Sylow subgroups is replaced by a suitable normalizer condition. In an earlier papar, one of the authors showed that the nilpotent length of a GSTG cannot exceed the number of distinct primes which divide the order of the group. The present investigation utilizes the ‘type’ of a GSTG to obtain improved bounds for the nilpotent length of a G,STG. It is also shown that a GSTG with nilpotent length n possesses a Hall subgroup of nilpotent length n which is a Sylow tower group.

Mathematical Subject Classification 2000
Primary: 20D20
Received: 29 February 1972
Revised: 19 June 1972
Published: 1 April 1973
James B. Derr
N. P. Mukherjee