Geodesic
Power-Rich and Power-Deficient LCA Groups
Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 664-670

Voir la notice de l'article provenant de la source Cambridge University Press

In [4], Edwin Hewitt denned a-rich LCA (i.e., locally compact abelian) groups and classified them by their algebraic structure. In this paper, we study LCA groups with some properties related to a-richness. We define an LCA group G to be power-rich if for every open neighbourhood V of the identity in G and for every integer n > 1, λ(nV) > 0, where nV = {nx ∈ G : x ∈ V} and λ is a Haar measure on G. G is power-meagre if for every integer n > 1, there is an open neighbourhood V of the identity, possibly depending on n, such that λ(nV) = 0. G is power-deficient if for every integer n > 1 and for every open neighbourhood V of the identity such that is compact, . G is dual power-rich if both G and Ĝ are power-rich. We define dual power-meagre and dual power-deficient groups similarly. 
Khan, M. A. Power-Rich and Power-Deficient LCA Groups. Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 664-670. doi: 10.4153/CJM-1981-052-6
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