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ABSTRACT
In [Citation[1], Theorem A], Beidleman and Robinson proved that if a group satisfies the permutizer condition, it is soluble, its chief factors have order a prime number or and
induces the full group of automorphisms in the chief factors of order
. In this paper, we show that the converse of this theorem is false by showing some counterexamples. We also find some sufficient conditions for a group satisfying the converse of that theorem to satisfy the permutizer condition.
ACKNOWLEDGMENT
Supported by Proyecto PB97-0674-C02-02 and Proyecto PB97-0604 from DGICYT, Ministerio de Educacio´n y Ciencia.