Examples of abelian

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We start with some general remarks on abelian invariants.
Attaching an abelian block is also often called extending a centralizer.
Yet nowhere is the reader told that actually abelian groups are not just abstract things but very tangible ones (namely direct sums of cyclic groups).
Since the action is rotation on a compact abelian group it has discrete spectrum and entropy zero.
For example, every finitely generated abelian group is amenable.
It can be seen, on the other hand, that it is possible to have abelian groups of automorphisms acting ergodically, without the group being compact.
Filling area conjecture, optimal systolic inequalities, and the fiber class in abelian covers.
It now has o several interesting generalizations in the abelian case in various directions.
Indeed, it is sufficient to prove this in the case of abelian varieties.
Since every subgroup of a finitely generated free abelian group is finitely generated, ker n will be finitely generated.
The chain group in dimension n is defined to be the free abelian group with basis the n-simplexes.
The nd torus is an abelian group, implying that the nd torus-hypergraph is translationinvariant (any two points 'look the same').
Since the group is abelian, the infranilmanifold is finitely covered by a torus.
These assumptions hold in particular if the categories are abelian, and one of the two functors is exact and faithful.

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