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Licensed Unlicensed Requires Authentication Published by De Gruyter October 17, 2017

A remark on spherical equations in free metabelian groups

  • Evgeny I. Timoshenko ORCID logo EMAIL logo

Abstract

I. Lysenok and A. Ushakov proved that the Diophantine problem for spherical quadric equations in free metabelian groups is solvable. The present paper proves this result by using the Magnus embedding.

MSC 2010: 20F16; 20F70

Award Identifier / Grant number: 15-01-01485

Funding statement: The author was partially supported by RFBR grant 15-01-01485.

References

[1] I. Lysenok and A. Ushakov, Spherical quadratic equations in free groups, Proc. Amer. Math. Soc. 144 (2016), 1383–1390. 10.1090/proc/12662Search in Google Scholar

[2] V. A. Roman’kov, Equations in free metabelian group, Sib. Math. J. 20 (1979), 469–471. 10.1007/BF00969959Search in Google Scholar

[3] V. Roman’kov, Equations over groups, Groups Complex. Cryptol. 4 (2012), 191–239. 10.1515/gcc-2012-0015Search in Google Scholar

Received: 2017-3-27
Revised: 2017-7-27
Published Online: 2017-10-17
Published in Print: 2017-11-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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