# Questions tagged [exceptional-isomorphisms]

Isomorphisms between members of infinite families of mathematical objects (finite simple groups, Lie groups etc), that are not examples of a pattern of such isomorphisms.

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### mathamatical structure where a bijection is not an isomorphism

During a lecture in module theory, my lecturer mentioned that not in all mathematical structures have the property where a function is an isomorphism if and only if it is a bijection, although this is ...
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### Is the seven-dimensional cross product unique?

I'm confused about how many different 7D cross products there are. I'm defining a 7D cross product to be any bilinear map $V \times V \to V$ (where $V$ is the inner product space $\mathbb{R}^7$ ...
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### Show that $\mathfrak{so}(4)\cong \mathfrak{so}(3)\oplus \mathfrak{so}(3)$ [duplicate]

I want to show that $\mathfrak{so}(4)\cong \mathfrak{so}(3)\oplus \mathfrak{so}(3)$. I know that as lie groups $SO(4)\cong (SU(2)\times SU(2))/\mathbb{Z}_2$ and that as $SU(2)/\mathbb{Z}_2 \cong SO(3)$...
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### Is SU(2) a subgroup of the exceptional lie group $G_2$?

I am not an expert in Lie groups and I have spent ages looking at textbooks; I assume that because I haven't found this statement explicitly it must either be untrue or obvious ;) The only thing I ...
• 108
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### $SL_2(\mathbb Z_3)/Z(SL_2(\mathbb Z_3)) \cong A_4$

I am trying to prove that the quotient group $SL_2(\mathbb Z_3)/Z(SL_2(\mathbb Z_3))$ is isomorphic to $A_4$. I could show that $SL_2(\mathbb Z_3)$ has $24$ elements (one can see this calculating all ...
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• 117
### Abstract Algebra: Find a number of non-isomorphic subgroup of $S_3$
I'm having difficulty in understanding the method to find the solution for this question. I repeat Question: Find the number of non-isomorphic subgroup of $S_3$ So is this the way to find the ...