Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

Groups in which every maximal partial order is exhaustive


Author: Gary J. Sherman
Journal: Proc. Amer. Math. Soc. 40 (1973), 83-86
MSC: Primary 06A55
DOI: https://doi.org/10.1090/S0002-9939-1973-0318033-6
MathSciNet review: 0318033
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be a group. A partial order $ P$ on $ G$ is exhaustive if each nongeneralized periodic element of $ G$ is either positive or negative with respect to $ P$. The class of groups on which every maximal partial order is exhaustive is characterized and shown to be closed under homomorphisms. An example is given to show that the class of groups on which every maximal right partial order is exhaustive is not closed under direct products.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06A55

Retrieve articles in all journals with MSC: 06A55


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0318033-6
Keywords: Exhaustively ordered group, partially ordered group, generalized group periodicity, nilpotent group
Article copyright: © Copyright 1973 American Mathematical Society