List questions from exceptional-isomorphisms

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Why is $\operatorname{Spin}(3) \cong \operatorname{SU}(2)$?

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209

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Why are these elements generators of cyclic groups?

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679

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In $D_4$, find $H_1$ isomorphic to $\mathbb{Z}_4$ and $H_2$ isomorphic to the Klein Four Group with $D_4/H_1$ isomorphic to $D_4/H_2$.

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Give an isomorphism between the linear spaces $U\times V$ and $L(U,V)$

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336

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How to count the conjugates of an exotic $S_5$?

Published on 18 Mar 2026 - 7:27

482

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About Fano plane symmetries

Published on 19 Aug 2020 - 10:17

96

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Different Lie groups of the same exceptional Lie algebra? for $\mathfrak{g_2,f_4,e_6,e_7,e_8}$

Published on 22 Aug 2020 - 15:34

72

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Extending the action $S_5$ on $2$-subsets of $\{1,\cdots,5\}$ to an action of $S_6$.

Published on 31 Oct 2020 - 19:17

178

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Categorifying $1^2+2^2+3^2+\cdots+24^2=70^2$

Published on 22 Mar 2026 - 20:19

285

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Implications of $\text{Spin}(3)\times \text{Spin}(3) \cong \text{Spin}(4)$

Published on 09 Mar 2021 - 3:17

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Dimensional coincidences between Lie groups

Published on 14 Mar 2021 - 22:33

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The Homogeneous Space $SO^+(1,3)/ \text{Sim}(2)$

Published on 01 Apr 2021 - 15:54

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transitive action from $A_5$ on a set of $6$ elements

Published on 06 Apr 2021 - 19:01

55

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Permutations of a $4\times4$ grid generated by permutations of rows, columns, and $2\times2$ quadrants

Published on 10 Jun 2021 - 21:14

List Question

Elementary isomorphism between $\operatorname{PSL}(2,5)$ and $A_5$

Why is $\operatorname{Spin}(3) \cong \operatorname{SU}(2)$?

Why are these elements generators of cyclic groups?

In $D_4$, find $H_1$ isomorphic to $\mathbb{Z}_4$ and $H_2$ isomorphic to the Klein Four Group with $D_4/H_1$ isomorphic to $D_4/H_2$.

Give an isomorphism between the linear spaces $U\times V$ and $L(U,V)$

How to count the conjugates of an exotic $S_5$?

About Fano plane symmetries

Different Lie groups of the same exceptional Lie algebra? for $\mathfrak{g_2,f_4,e_6,e_7,e_8}$

Extending the action $S_5$ on $2$-subsets of $\{1,\cdots,5\}$ to an action of $S_6$.

Categorifying $1^2+2^2+3^2+\cdots+24^2=70^2$

Implications of $\text{Spin}(3)\times \text{Spin}(3) \cong \text{Spin}(4)$

Dimensional coincidences between Lie groups

The Homogeneous Space $SO^+(1,3)/ \text{Sim}(2)$

transitive action from $A_5$ on a set of $6$ elements

Permutations of a $4\times4$ grid generated by permutations of rows, columns, and $2\times2$ quadrants

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