Abstract
In 2011, while investigating fundamental groups of wild spaces, K.Eda [Citation7] showed that the fundamental group of the Hawaiian earring (the Hawaiian earring group, in short) has the property that for any homomorphism h from it to a free product A*B, there exists a natural number N such that
is contained in a conjugate subgroup to A or B. In the present article, we prove a corresponding property for certain HNN extensions and amalgamated free products. This allows us to show that some one-relator groups, including Baumslag–Solitar groups, are n-slender.
2010 Mathematics Subject Classification:
ACKNOWLEDGMENTS
I would like to thank to Prof. Katsuya Eda for giving helpful advice. I also thank the members of the seminar within the Eda Laboratory.
Notes
1There is a straightforward generalization of slenderness to noncommutative groups G [Citation11]. But it depends on only abelian subgroups of G. The property of n-slenderness is essentially different from it.
Communicated by M. Kambites.