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searching for Finitely generated abelian group 6 found (37 total)

alternate case: finitely generated abelian group

Mordell–Weil group (1,164 words) [view diff] no match in snippet view article find links to article

the Mordell–Weil theorem which shows this group is in fact a finitely-generated abelian group. Moreover, there are many conjectures related to this group

Gromov's theorem on groups of polynomial growth (967 words) [view diff] exact match in snippet view article find links to article

G_{2}\supseteq \cdots .} In particular, the quotient group Gk/Gk+1 is a finitely generated abelian group. The Bass–Guivarc'h formula states that the order of polynomial

Smooth completion (656 words) [view diff] exact match in snippet view article find links to article

the units of the ring of regular functions O(X) on X is a finitely generated abelian group of rank r -1. Suppose the base field is perfect. Any affine

Pure subgroup (692 words) [view diff] exact match in snippet view article find links to article

directed union of pure subgroups is a pure subgroup. Since in a finitely generated abelian group the torsion subgroup is a direct summand, one might ask if

Character group (1,506 words) [view diff] exact match in snippet view article find links to article

^{2n}/\mathbb {Z} ^{2n}} which is the expected result. Since every finitely generated abelian group is isomorphic to G ≅ Z n ⊕ ⨁ i = 1 m Z / a i {\displaystyle

Adams spectral sequence (3,283 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle i<0} and π i ( X ) {\displaystyle \pi _{i}(X)} is a finitely generated Abelian group in each degree. Then, there is a spectral sequence E ∗ ∗ ,