An Archimedian property for groups with polynomial growth

Shobana Ganesan, Joe Jenkins

Type: Article

Publication Date: 1983-01-01

Citations: 2

DOI: https://doi.org/10.1090/s0002-9939-1983-0699432-6

Abstract

The notion of Archimedian group is introduced. It is shown that if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is either a finitely generated, solvable group or a connected, locally compact group, then <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is Archimedian if it has polynomial growth. A partial converse is also proven.

Locations

Proceedings of the American Mathematical Society - View - PDF

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