List questions from infinite-groups

Published on 10 Dec 2012 - 9:52

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countable group, uncountably many distinct subgroup?

Published on 12 Dec 2012 - 16:18

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Find an abelian infinite group such that every proper subgroup is finite

Published on 18 Dec 2012 - 2:47

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Use a group-theoretic proof to show that $\mathbb{Q}^$ under multiplication is not isomorphic to $\mathbb{R}^$ under multiplication.

Published on 19 Aug 2020 - 12:26

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finite groups are subgroups of the infinite one

Published on 27 Mar 2026 - 2:02

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Find a finite subgroup of order at least $6$ from an infinite non-abelian group which every element is of order less than $6$.

Published on 09 Sep 2020 - 1:10

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Writing element of infinite direct product of abelian groups as an infinite sum

Published on 11 Sep 2020 - 3:23

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proving group is infinite

Published on 19 Sep 2020 - 0:36

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Are infinite cyclic normal subgroups "virtually" central?

Published on 30 Sep 2020 - 21:33

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When are free abelian normal subgroups "virtually" central?

Published on 26 Mar 2026 - 19:35

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Identifying the quotient class of infinite group under the classification of finitely generated abelian groups.

Published on 01 Oct 2020 - 22:47

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How can Cyclic groups be infinite

Published on 04 Oct 2020 - 2:38

717

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Find smallest subgroups

Published on 07 Oct 2020 - 21:55

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The order of elements in infinite quotient groups

Published on 14 Oct 2020 - 21:52

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Understanding the free product amalgamation with an example

Published on 26 Mar 2026 - 2:58

List Question

An infinite $p$-group may not be nilpotent

countable group, uncountably many distinct subgroup?

Find an abelian infinite group such that every proper subgroup is finite

Use a group-theoretic proof to show that $\mathbb{Q}^$ under multiplication is not isomorphic to $\mathbb{R}^$ under multiplication.

finite groups are subgroups of the infinite one

Find a finite subgroup of order at least $6$ from an infinite non-abelian group which every element is of order less than $6$.

Writing element of infinite direct product of abelian groups as an infinite sum

proving group is infinite

Are infinite cyclic normal subgroups "virtually" central?

When are free abelian normal subgroups "virtually" central?

Identifying the quotient class of infinite group under the classification of finitely generated abelian groups.

How can Cyclic groups be infinite

Find smallest subgroups

The order of elements in infinite quotient groups

Understanding the free product amalgamation with an example

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