## Frattini subgroups of $3$-manifold groups

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- by R. B. J. T. Allenby, J. Boler, B. Evans, L. E. Moser and C. Y. Tang
- Trans. Amer. Math. Soc.
**247**(1979), 275-300 - DOI: https://doi.org/10.1090/S0002-9947-1979-0517695-8
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## Abstract:

In this paper it is shown that if the Frattini subgroup of the fundamental group of a compact, orientable, irreducible, sufficiently large 3-manifold is nontrivial then the 3-manifold is a Seifert fibered space. We show further that the Frattini subgroup of the group of a Seifert fibered space is trivial or cyclic. As a corollary to our work we prove that every knot group has trivial Frattini subgroup.## References

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## Bibliographic Information

- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**247**(1979), 275-300 - MSC: Primary 57M05; Secondary 20F34
- DOI: https://doi.org/10.1090/S0002-9947-1979-0517695-8
- MathSciNet review: 517695