Let g,c denote positive integers. A group is said to have type (g→c) if every subgroup which can be generated by g elements is nilpotent of class at most c. A result of R. H. Bruck shows that groups of type (4→5) without elements of order 2 are nilpotent of class at most 7. In the present paper the following result is reported: If G is a (4→5) group on 5 generators without elements of order 2, then G is nilpotent of class at most 6.
Proceedings of the Iowa Academy of Science
©1964 Iowa Academy of Science, Inc.
Pilgrim, Donald H.
"Engel Conditions on Groups,"
Proceedings of the Iowa Academy of Science, 71(1), 377-383.
Available at: https://scholarworks.uni.edu/pias/vol71/iss1/55