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Proceedings of the American Mathematical Society

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

 
 

 

On $2$-knot groups with abelian commutator subgroups


Author: Katsuyuki Yoshikawa
Journal: Proc. Amer. Math. Soc. 92 (1984), 305-310
MSC: Primary 57Q45
DOI: https://doi.org/10.1090/S0002-9939-1984-0754727-3
MathSciNet review: 754727
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Abstract: In this paper it is shown that if the commutator subgroup of a $2$-knot group is abelian, then it is isomorphic to $Z \oplus Z \oplus Z$, ${Z_\alpha }$, $Z[1/2]$ or $Z[1/2] \oplus {Z_5}$, where $\alpha$ is an odd integer and $Z[1/2]$ is the additive group of the dyadic rationals.


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Keywords: <IMG WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$2$">-knot, abelian commutator subgroup
Article copyright: © Copyright 1984 American Mathematical Society