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1. • CommentRowNumber1.
   • CommentAuthorTim_Porter
   • CommentTimeOct 2nd 2018
   • (edited Oct 2nd 2018)
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexAdded in the usual group presentation of the dihedral group $D_{2n}$ plus a warning that this group is also denoted $D_n$ by some authors (including myself!!!) <a href="https://ncatlab.org/nlab/revision/diff/dihedral+group/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/dihedral+group/16">v16</a>, <a href="https://ncatlab.org/nlab/show/dihedral+group">current</a>

   Added in the usual group presentation of the dihedral group $D_{2n}$ plus a warning that this group is also denoted $D_n$ by some authors (including myself!!!)

   diff, v16, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeOct 2nd 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexYeah, notation can be a bit of a pain here. I have given your remark a remark-environment [here](https://ncatlab.org/nlab/show/dihedral+group#NotationConvention), instead of it being a subsection, and edited slightly, mostly for formatting.

   Yeah, notation can be a bit of a pain here.

   I have given your remark a remark-environment here, instead of it being a subsection, and edited slightly, mostly for formatting.

3. • CommentRowNumber3.
   • CommentAuthorTim_Porter
   • CommentTimeOct 2nd 2018
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexGreat

   Great

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeOct 4th 2018
   • (edited Oct 4th 2018)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded mentioning, pointers, and redirects for "dicyclic group", synonymous to "binary dihedral group" <a href="https://ncatlab.org/nlab/revision/diff/dihedral+group/18">diff</a>, <a href="https://ncatlab.org/nlab/revision/dihedral+group/18">v18</a>, <a href="https://ncatlab.org/nlab/show/dihedral+group">current</a>

   added mentioning, pointers, and redirects for “dicyclic group”, synonymous to “binary dihedral group”

   diff, v18, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeFeb 13th 2019
   • (edited Feb 13th 2019)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded some actual explicit details on the definition of the binary dihedral groups ([here](https://ncatlab.org/nlab/show/dihedral+group#BinaryDihedralGroup)) <a href="https://ncatlab.org/nlab/revision/diff/dihedral+group/21">diff</a>, <a href="https://ncatlab.org/nlab/revision/dihedral+group/21">v21</a>, <a href="https://ncatlab.org/nlab/show/dihedral+group">current</a>

   added some actual explicit details on the definition of the binary dihedral groups (here)

   diff, v21, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeDec 21st 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexmade explicit ([here](https://ncatlab.org/nlab/show/dihedral+group#ShortExactSequence)) the short exact sequence $1 \to \mathbb{Z}/n \to D_{2n} \to \mathbb{Z}/2 \to 1$. <a href="https://ncatlab.org/nlab/revision/diff/dihedral+group/27">diff</a>, <a href="https://ncatlab.org/nlab/revision/dihedral+group/27">v27</a>, <a href="https://ncatlab.org/nlab/show/dihedral+group">current</a>

   made explicit (here) the short exact sequence $1 \to \mathbb{Z}/n \to D_{2n} \to \mathbb{Z}/2 \to 1$.

   diff, v27, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeJul 6th 2022
   • (edited Jul 6th 2022)
   • PermaLink
   Author: Urs
   Format: MarkdownItexIs there a citable computation of the group cohomology of dihedral groups with coefficients in $\mathbb{Z}$ equipped with its non-trivial sign action? This question is also [MO:q/141489](https://mathoverflow.net/q/141489/381). I haven't checked the two answers there yet, but don't they contradict each other? The accepted answer [MO:a/141557](https://mathoverflow.net/a/141557/381) sees the cohomology concentrated in odd degrees. But the other answer [MO:a/141546](https://mathoverflow.net/a/141546/381), whose author claims to have checked this with computer algebra, argues for a nontivial contribution in degree 2.

   Is there a citable computation of the group cohomology of dihedral groups with coefficients in $\mathbb{Z}$ equipped with its non-trivial sign action?

   This question is also MO:q/141489.

   I haven’t checked the two answers there yet, but don’t they contradict each other?

   The accepted answer MO:a/141557 sees the cohomology concentrated in odd degrees.

   But the other answer MO:a/141546, whose author claims to have checked this with computer algebra, argues for a nontivial contribution in degree 2.