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Formation theory and groups of automorphisms of -groups*

Published online by Cambridge University Press:  14 February 2012

M. J. Tomkinson
M. J. Tomkinson
Affiliation:
Department of Mathematics, University of Glasgow
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Synopsis

Further results from the theory of finite soluble groups are extended to the class of locally finite groups with a satisfactory Sylow structure. Let be a saturated U-formation and A a -group of automorphisms of the -group G. A is said to act -centrally on G if G has an A-composition series (Λσ/Vσ; σ ∈ ∑) such that A induces an f(p)-group of automorphisms in each p-factor Λσ/Vσ. We show that in this situation A is an -group, thus generalising the result of Schmid [8]. Associated results of Schmid and of Baer are also extended to the infinite case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 76 , Issue 4 , 1977 , pp. 255 - 265
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

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