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Removed the deprecated (abstract-algebra) tag - see the tag info: https://mathoverflow.net/tags/abstract-algebra/info (if there are some other suitable tags, choose them instead.)
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Martin Sleziak
Martin Sleziak
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clarify, since there are two conventions for "$D_n$"
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Arturo Magidin
Arturo Magidin
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What is the automorphism group of direct sum of dihedral group of order $8$, $D_4$?

For example, $\mathrm{Aut}(D_4)$ is isomorphic to $D_4$. How about $\mathrm{Aut}(D_4\times D_4)$, $\mathrm{Aut}(D_4\times D_4\times D_4)$, and $\mathrm{Aut}(D_4\times D_4 \times D_4 \times D_4)$?

What is the automorphism group of direct sum of dihedral group $D_4$?

For example, $\mathrm{Aut}(D_4)$ is isomorphic to $D_4$. How about $\mathrm{Aut}(D_4\times D_4)$, $\mathrm{Aut}(D_4\times D_4\times D_4)$, and $\mathrm{Aut}(D_4\times D_4 \times D_4 \times D_4)$?

What is the automorphism group of direct sum of dihedral group of order $8$, $D_4$?

For example, $\mathrm{Aut}(D_4)$ is isomorphic to $D_4$. How about $\mathrm{Aut}(D_4\times D_4)$, $\mathrm{Aut}(D_4\times D_4\times D_4)$, and $\mathrm{Aut}(D_4\times D_4 \times D_4 \times D_4)$?

LaTeX, cleared up title
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Arun Debray
Arun Debray
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What isare the automorphism groupgroups of direct sumproducts of dihedral group D4

What is the automorphism group of direct sum of dihedral group D(4)$D_4$?

For example, Aut(D4)$\mathrm{Aut}(D_4)$ is isomorphic to D4$D_4$. How about Aut(D4xD4)$\mathrm{Aut}(D_4\times D_4)$, Aut(D4xD4xD4)$\mathrm{Aut}(D_4\times D_4\times D_4)$, Aut(D4xD4xD4xD4).and $\mathrm{Aut}(D_4\times D_4 \times D_4 \times D_4)$?

What is the automorphism group of direct sum of dihedral group D4

What is the automorphism group of direct sum of dihedral group D(4)?

For example, Aut(D4) is isomorphic to D4. How about Aut(D4xD4), Aut(D4xD4xD4), Aut(D4xD4xD4xD4).

What are the automorphism groups of direct products of dihedral group D4

What is the automorphism group of direct sum of dihedral group $D_4$?

For example, $\mathrm{Aut}(D_4)$ is isomorphic to $D_4$. How about $\mathrm{Aut}(D_4\times D_4)$, $\mathrm{Aut}(D_4\times D_4\times D_4)$, and $\mathrm{Aut}(D_4\times D_4 \times D_4 \times D_4)$?

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Sirui Lu
Sirui Lu
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