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The FC-Chain of a Group

Published online by Cambridge University Press:  20 November 2018

Franklin Haimo
Franklin Haimo*
Affiliation:
Washington University , Saint Louis, Missouri
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Baer [2] and Neumann [5] have discussed groups in which there is a limitation on the number of conjugates which an element may have. For a given group G, let H1 be the set of all elements of G which have only a finite number of conjugates in G, let H2 be the set of those elements of G, the conjugates of each of which lie in only a finite number of cosets of H1 in G; and in this fashion define H3, H4, …. We shall show that the Hi are strictly characteristic subgroups of G.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 498 - 511
Copyright
Copyright © Canadian Mathematical Society 1953

References

1. Baer, Reinhold, Representations of groups as quotient groups I, Trans. Amer. Math. Soc, 58 (1945), 295–347.Google Scholar
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3. Baer, Reinhold, Endlichkeitskriterien fur Kommutatorgruppen, Math. Ann. 124 (1952), 161–177.Google Scholar
4. Kuros, A. G., Teoriya grupp (Moscow-Leningrad, 1944).Google Scholar
5. Neumann, B. H., Groups with finite classes of conjugate elements, Proc. London Math. Soc. (3), 1 (1951), 178–187.Google Scholar
6. Zassenhaus, Hans, The theory of groups (New York, 1949).Google Scholar