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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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 PDF
Trans. Amer. Math. Soc. 247 (1979), 275-300 Request permission

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.
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Additional 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