List questions from group-isomorphism

Published on 04 Apr 2026 - 12:44

54

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Why can't the Klein-4 group be generated by a single element?

Published on 17 Oct 2017 - 2:20

1.3k

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How to construct an isomorphism?

Published on 19 Oct 2017 - 22:21

705

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The order of inner automorphisms of $D_4$ is 2

Published on 20 Oct 2017 - 11:36

80

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An identity is true for finite permutation groups, but is it true for infinite ones?

Published on 27 Mar 2026 - 16:09

968

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What's the relation between real and quaternionic symplectic group

Published on 23 Oct 2017 - 15:32

975

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Prove the given function is an isomorphism and well-defined

Published on 25 Oct 2017 - 5:36

1.2k

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How Cyclic Group of order 6 is isomorphic to the product of cyclic groups of order 2 and 3. How to generalize this.

Published on 04 Apr 2026 - 2:34

320

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Show that Cayley's theorem, when applied to $\mathbb{R}$, produces the subgroup of $S_{\mathbb{R}}$ which contains all translations of the real line

Published on 25 Oct 2017 - 23:40

45

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If $j:K→K'$ is a field isomorphism, what is the meaning of $j(p)$, being $p$ a polynomial over $K$.

Published on 26 Oct 2017 - 1:20

1k

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Prove that the map of $A \mapsto BAB^{-1}$ is an automorphism of the group of all Special Matrices $SL(\mathbb{R})$

Published on 30 Mar 2026 - 20:45

102

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Proof normal divider of two sets?

Published on 26 Oct 2017 - 7:13

474

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Showing these two groups are both non-isomorphic, non abelian and have order 12

Published on 27 Oct 2017 - 13:59

95

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Show $G$ is isomorphic to $\mathbb{Z}$

Published on 27 Mar 2026 - 6:07

735

Views

can someone help me understand this solution (introductory discrete math)

Published on 31 Oct 2017 - 0:28

List Question

Homomorphic image of $S_{8}$

Why can't the Klein-4 group be generated by a single element?

How to construct an isomorphism?

The order of inner automorphisms of $D_4$ is 2

An identity is true for finite permutation groups, but is it true for infinite ones?

What's the relation between real and quaternionic symplectic group

Prove the given function is an isomorphism and well-defined

How Cyclic Group of order 6 is isomorphic to the product of cyclic groups of order 2 and 3. How to generalize this.

Show that Cayley's theorem, when applied to $\mathbb{R}$, produces the subgroup of $S_{\mathbb{R}}$ which contains all translations of the real line

If $j:K→K'$ is a field isomorphism, what is the meaning of $j(p)$, being $p$ a polynomial over $K$.

Prove that the map of $A \mapsto BAB^{-1}$ is an automorphism of the group of all Special Matrices $SL(\mathbb{R})$

Proof normal divider of two sets?

Showing these two groups are both non-isomorphic, non abelian and have order 12

Show $G$ is isomorphic to $\mathbb{Z}$

can someone help me understand this solution (introductory discrete math)

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