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• CommentRowNumber1.
• CommentAuthorTim_Porter
• CommentTimeOct 2nd 2018
• (edited Oct 2nd 2018)

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!!!)

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeOct 2nd 2018

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.

• CommentRowNumber3.
• CommentAuthorTim_Porter
• CommentTimeOct 2nd 2018

Great

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeOct 4th 2018
• (edited Oct 4th 2018)

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

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeFeb 13th 2019
• (edited Feb 13th 2019)

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

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeDec 21st 2021

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

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJul 6th 2022
• (edited Jul 6th 2022)

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.