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THE $3k-4$ THEOREM FOR ORDERED GROUPS

Part of: Additive number theory; partitions

Published online by Cambridge University Press:  28 September 2017

PREM PRAKASH PANDEY Open the ORCID record for PREM PRAKASH PANDEY [Opens in a new window]
PREM PRAKASH PANDEY*
Affiliation:
Department of Mathematics, IISER Berhampur, Government ITI Berhampur, Khodasingi, Berhampur-760010, India email premshivaganga@gmail.com
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Abstract

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Recently, Freiman et al. [‘Small doubling in ordered groups’, J. Aust. Math. Soc. 96(3) (2014), 316–325] proved two ‘structure theorems’ for ordered groups. We give elementary proofs of these two theorems.

Keywords

3k - 4 theoremordered groups

MSC classification

Primary: 11P70: Inverse problems of additive number theory, including sumsets
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 1 , February 2018 , pp. 43 - 46
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

References

Freiman, G. A., Herzog, M., Longobardi, P. and Maj, M., ‘Small doubling in ordered groups’, J. Aust. Math. Soc. 96(3) (2014), 316–325.Google Scholar
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Freiman, G. A., Herzog, M., Longobardi, P., Maj, M., Plagne, A. and Stanchescu, Y. V., ‘Small doubling in ordered groups: generators and structures’, Groups Geom. Dyn. 11(2) (2017), 585–612.Google Scholar
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