Two-generator groups with perfect Frattini subgroups

Evans, M. J.

doi:10.1090/S0002-9939-1987-0883395-8

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Two-generator groups with perfect Frattini subgroups
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by M. J. Evans PDF

Proc. Amer. Math. Soc. 100 (1987), 25-28 Request permission

Abstract:

In this paper, $2$-generator groups with perfect Frattini subgroups are constructed. The construction also shows that every countable group can be embedded in the Frattini subgroup of a $2$-generator group.

References

P. Hall, The Frattini subgroups of finitely generated groups, Proc. London Math. Soc. (3) 11 (1961), 327–352. MR 124406, DOI 10.1112/plms/s3-11.1.327
Roger C. Lyndon and Paul E. Schupp, Combinatorial group theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 89, Springer-Verlag, Berlin-New York, 1977. MR 0577064