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The Fitting subgroup of a linear solvable group

Published online by Cambridge University Press:  09 April 2009

John D. Dixon
John D. Dixon
Affiliation:
University of New South WalesKensington, N.S.W.
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Let G be a group. The Fitting subgroup F(G) of G is defined to be the set union of all normal nilpotent subgroups of G. Since the product of two normal nilpotent subgroups is again a normal nilpotent subgroup (see [10] p. 238), F(G) is the unique maximal normal, locally nilpotent sungroup of G. In particular, is G is finite, then F(G) is the unique maximal normal nilpotent subgroup of G. If G is a notrivial solvable group, then clearly F(G) ≠1.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 4 , November 1967 , pp. 417 - 424
Copyright
Copyright © Australian Mathematical Society 1967

References

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