List questions from group-isomorphism

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Showing that $2$ of the following groups are not isomorphic

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When can the isomorphism theorem for Groups be rewritten as a direct product?

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54

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Smallest $n\in \mathbb{Z}_{>0}$ for existence of a monomorphism $G \rightarrow S_n$

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$\mathrm{Hom}(\mathrm{Hom}(G,H),H) \simeq G$?

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Do the results hold for isomorphisms of groups?

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322

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Isomorphism about direct product of multiplicative group and direct product of additive group

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31

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Direct Sums of Abelian Groups/$R$-Modules

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61

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Injective Morphisms of Modules and Bases

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116

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Suppose$f:S_{3}\longrightarrow R^{\ast}$is Homomorphism.Then Kernal of h has

Published on 28 Mar 2026 - 12:30

587

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How to Count Homomorphism from any finite group G to infinite cyclic group?

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Show that the groups $G$ and $\langle G, * \rangle$ are isomorphic.

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Prove that the function $f:G \to G$ given by $f(a)=a^k$ is an isomorphism.

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Show that $A_5$ has no subgroup of order $20$.

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810

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Proving U(33) is isomorphic to $Z_{10}\oplus Z_2$?

Published on 26 Mar 2026 - 11:17

List Question

Symmetries of the Tetrahedron - Geometric description and isomorphic correlations

Showing that $2$ of the following groups are not isomorphic

When can the isomorphism theorem for Groups be rewritten as a direct product?

Smallest $n\in \mathbb{Z}_{>0}$ for existence of a monomorphism $G \rightarrow S_n$

$\mathrm{Hom}(\mathrm{Hom}(G,H),H) \simeq G$?

Do the results hold for isomorphisms of groups?

Isomorphism about direct product of multiplicative group and direct product of additive group

Direct Sums of Abelian Groups/$R$-Modules

Injective Morphisms of Modules and Bases

Suppose$f:S_{3}\longrightarrow R^{\ast}$is Homomorphism.Then Kernal of h has

How to Count Homomorphism from any finite group G to infinite cyclic group?

Show that the groups $G$ and $\langle G, * \rangle$ are isomorphic.

Prove that the function $f:G \to G$ given by $f(a)=a^k$ is an isomorphism.

Show that $A_5$ has no subgroup of order $20$.

Proving U(33) is isomorphic to $Z_{10}\oplus Z_2$?

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