List questions from direct-product

Published on 24 Mar 2021 - 4:09

125

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Kernel of $\phi \colon $Hom$_R(\prod_{i \in I}A_i, B) \to \prod_{i \in I}\text{Hom}_R(A_i, B)$ is isomorphic to Hom$_R(\prod A_i/\sum^\oplus A_i, B)$.

Published on 25 Mar 2026 - 5:10

85

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Hungerford's notation of $(|G|,|H|)=1$.

Published on 29 Mar 2021 - 1:30

161

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Prove two Hom are isomorphic for a torsion R-module where R is a PID

Published on 29 Mar 2021 - 12:54

65

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Product of groups satisfying ACC again satisfies ACC?

Published on 31 Mar 2021 - 17:23

87

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Free group on $\{x,y\}$ and Group $\mathbb Z\times \mathbb Z$

Published on 27 Mar 2026 - 14:39

329

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Cancellation property for direct products

Published on 02 Apr 2021 - 11:18

152

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What are the invariant factors of $G \times G$?

Published on 10 Apr 2021 - 18:33

37

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Characterization of permutable subgroups (direct product)

Published on 12 Apr 2021 - 18:31

86

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Show that for any prime $p$, $\mathbb{Q}/\mathbb{Z} = H \times K$

Published on 19 Apr 2021 - 1:35

78

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Are these two infinite groups isomorphic?

Published on 28 Mar 2026 - 0:27

110

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Does $\left(\prod_iM_i\right)/\left(\prod_iS_i\right)\cong \prod_{i\in I}\left(M_i/S_i\right)$ hold for modules?

Published on 21 Apr 2021 - 15:28

59

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Changing the order of the Cartesian Product defines an homomorphism?

Published on 23 Apr 2021 - 14:01

190

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Infinite product not free

Published on 27 Mar 2026 - 1:13

407

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Why is $C_4 \times C_4$ not isomorphic to $C_4 \times C_2 \times C_2$?

Published on 30 Apr 2021 - 20:19

List Question

Find all subgroups of $\mathbb{Z_7}\times\mathbb{Z_5}$

Kernel of $\phi \colon $Hom$_R(\prod_{i \in I}A_i, B) \to \prod_{i \in I}\text{Hom}_R(A_i, B)$ is isomorphic to Hom$_R(\prod A_i/\sum^\oplus A_i, B)$.

Hungerford's notation of $(|G|,|H|)=1$.

Prove two Hom are isomorphic for a torsion R-module where R is a PID

Product of groups satisfying ACC again satisfies ACC?

Free group on $\{x,y\}$ and Group $\mathbb Z\times \mathbb Z$

Cancellation property for direct products

What are the invariant factors of $G \times G$?

Characterization of permutable subgroups (direct product)

Show that for any prime $p$, $\mathbb{Q}/\mathbb{Z} = H \times K$

Are these two infinite groups isomorphic?

Does $\left(\prod_iM_i\right)/\left(\prod_iS_i\right)\cong \prod_{i\in I}\left(M_i/S_i\right)$ hold for modules?

Changing the order of the Cartesian Product defines an homomorphism?

Infinite product not free

Why is $C_4 \times C_4$ not isomorphic to $C_4 \times C_2 \times C_2$?

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