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A local characterisation of serial subgroups

Published online by Cambridge University Press:  20 January 2009

J. A. Hulse
J. A. Hulse
Affiliation:
Department of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Edinburgh, EH9 3JZ.
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In (2) Hickin and Phillips establish various results connecting the ideas of local systems and serial subgroups in group theory. In (4) Petty shows that if a group has a local factor system of -groups, then it may be embedded in an ultraproduct of -groups and he uses this result to extend some local theorems which were originally due to Mal'cev (3) and at the same time providing an elementary proof. We shall show that Petty's method may be used to prove results about seriality and local systems.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 3 , October 1979 , pp. 201 - 205
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

(1) Herstein, I. N., Noncommutative rings (Mathematical Association of America, Menascha, Wis., (1968)Google Scholar
(2) Hickin, K. K. and Phillips, R. E., On classes of groups defined by systems of subgroups, Arch. Math. (Basel) 24 (1973), 346–350.CrossRefGoogle Scholar
(3) Mal'cev, A. I., On a general method for obtaining local theorems in group theory, Ivanov. Gos. Ped. Inst. Učen. Zap. 1 (1941), 3–9.Google Scholar
(4) Petty, J. V., Classes of groups defined by series or normal factor coverings, J. Algebra 40 (1976), 610–617.CrossRefGoogle Scholar
(5) Robinson, D. J. S., Finiteness conditions and generalized soluble groups, part 2 (Springer-Verlag, Berlin, 1972).CrossRefGoogle Scholar