Geodesic
On finite powers of countably compact groups
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 3, pp. 617-626.

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We will show that under ${M\kern -1.8pt A\kern 0.2pt }_{countable}$ for each $k \in \Bbb N$ there exists a group whose $k$-th power is countably compact but whose $2^k$-th power is not countably compact. In particular, for each $k \in \Bbb N$ there exists $l \in [k,2^k)$ and a group whose $l$-th power is countably compact but the $l+1$-st power is not countably compact.
Classification : 22A05, 54A35, 54B10, 54D20, 54H11
Keywords: countable compactness; ${M\kern -1.8pt A\kern 0.2pt }_{countable}$; topological groups; finite powers 
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Tomita, Artur Hideyuki. On finite powers of countably compact groups. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 3, pp. 617-626. http://geodesic.mathdoc.fr/item/CMUC_1996__37_3_a18/