How do you call groups formed as direct sums of cyclic groups?
0
$begingroup$
What do you call groups of the form $mathbb{Z}oplusmathbb{Z}opluscdotsoplusmathbb{Z}/mathbb{Z}d_1oplusmathbb{Z}/mathbb{Z}d_2opluscdots$
These kind of groups usualy appear as homology groups.
Is it just a classification of abelian groups?
homology-cohomology abelian-groups
asked Jan 7 at 9:44
Jake B.Jake B.
1666
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add a comment |
0
$begingroup$
What do you call groups of the form $mathbb{Z}oplusmathbb{Z}opluscdotsoplusmathbb{Z}/mathbb{Z}d_1oplusmathbb{Z}/mathbb{Z}d_2opluscdots$
These kind of groups usualy appear as homology groups.
Is it just a classification of abelian groups?
homology-cohomology abelian-groups
asked Jan 7 at 9:44
Jake B.Jake B.
1666
$endgroup$
$begingroup$
Countably generated ablian group, maybe? I may be missing some subtleties here which will surely be pointed out to me.
$endgroup$
– Arthur
Jan 7 at 9:49
$begingroup$
I'm curious, where do these groups appear as the homology groups of some space?
$endgroup$
– Perturbative
Jan 7 at 12:37
$begingroup$
Just a guess but the nature of the groups you described seem to be related to statement of the fundamental theorem of finitely generated abelian groups, in which every finitely generated abelian group is classified in a similar nature : en.wikipedia.org/wiki/…
$endgroup$
– Perturbative
Jan 7 at 12:40
add a comment |
0
0
0
$begingroup$
What do you call groups of the form $mathbb{Z}oplusmathbb{Z}opluscdotsoplusmathbb{Z}/mathbb{Z}d_1oplusmathbb{Z}/mathbb{Z}d_2opluscdots$
These kind of groups usualy appear as homology groups.
Is it just a classification of abelian groups?
homology-cohomology abelian-groups
asked Jan 7 at 9:44
Jake B.Jake B.
1666
$endgroup$
What do you call groups of the form $mathbb{Z}oplusmathbb{Z}opluscdotsoplusmathbb{Z}/mathbb{Z}d_1oplusmathbb{Z}/mathbb{Z}d_2opluscdots$
These kind of groups usualy appear as homology groups.
Is it just a classification of abelian groups?
homology-cohomology abelian-groups
homology-cohomology abelian-groups
asked Jan 7 at 9:44
Jake B.Jake B.
1666
asked Jan 7 at 9:44
Jake B.Jake B.
1666
asked Jan 7 at 9:44
Jake B.Jake B.
1666
asked Jan 7 at 9:44
Jake B.Jake B.
1666
asked Jan 7 at 9:44
Jake B.Jake B.
1666
1666
$begingroup$
Countably generated ablian group, maybe? I may be missing some subtleties here which will surely be pointed out to me.
$endgroup$
– Arthur
Jan 7 at 9:49
$begingroup$
I'm curious, where do these groups appear as the homology groups of some space?
$endgroup$
– Perturbative
Jan 7 at 12:37
$begingroup$
Just a guess but the nature of the groups you described seem to be related to statement of the fundamental theorem of finitely generated abelian groups, in which every finitely generated abelian group is classified in a similar nature : en.wikipedia.org/wiki/…
$endgroup$
– Perturbative
Jan 7 at 12:40
add a comment |
$begingroup$
Countably generated ablian group, maybe? I may be missing some subtleties here which will surely be pointed out to me.
$endgroup$
– Arthur
Jan 7 at 9:49
$begingroup$
I'm curious, where do these groups appear as the homology groups of some space?
$endgroup$
– Perturbative
Jan 7 at 12:37
$begingroup$
Just a guess but the nature of the groups you described seem to be related to statement of the fundamental theorem of finitely generated abelian groups, in which every finitely generated abelian group is classified in a similar nature : en.wikipedia.org/wiki/…
$endgroup$
– Perturbative
Jan 7 at 12:40
$begingroup$
Countably generated ablian group, maybe? I may be missing some subtleties here which will surely be pointed out to me.
$endgroup$
– Arthur
Jan 7 at 9:49
$begingroup$
Countably generated ablian group, maybe? I may be missing some subtleties here which will surely be pointed out to me.
$endgroup$
– Arthur
Jan 7 at 9:49
$begingroup$
I'm curious, where do these groups appear as the homology groups of some space?
$endgroup$
– Perturbative
Jan 7 at 12:37
$begingroup$
I'm curious, where do these groups appear as the homology groups of some space?
$endgroup$
– Perturbative
Jan 7 at 12:37
$begingroup$
Just a guess but the nature of the groups you described seem to be related to statement of the fundamental theorem of finitely generated abelian groups, in which every finitely generated abelian group is classified in a similar nature : en.wikipedia.org/wiki/…
$endgroup$
– Perturbative
Jan 7 at 12:40
$begingroup$
Just a guess but the nature of the groups you described seem to be related to statement of the fundamental theorem of finitely generated abelian groups, in which every finitely generated abelian group is classified in a similar nature : en.wikipedia.org/wiki/…
$endgroup$
– Perturbative
Jan 7 at 12:40
add a comment |
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$begingroup$
Countably generated ablian group, maybe? I may be missing some subtleties here which will surely be pointed out to me.
$endgroup$
– Arthur
Jan 7 at 9:49
$begingroup$
I'm curious, where do these groups appear as the homology groups of some space?
$endgroup$
– Perturbative
Jan 7 at 12:37
$begingroup$
Just a guess but the nature of the groups you described seem to be related to statement of the fundamental theorem of finitely generated abelian groups, in which every finitely generated abelian group is classified in a similar nature : en.wikipedia.org/wiki/…
$endgroup$
– Perturbative
Jan 7 at 12:40