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Results tagged with gr.group-theory
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user 45255
Questions about the branch of algebra that deals with groups.
1
vote
All $2$-designs arising from the action of the affine linear group on the field of prime order
For fixed $k \ge 3$, the generic such design is a full orbit with "index" $\lambda = k(k-1)$ and is probably not of much (combinatorial) interest. Short orbits are, of course, very interesting. As a …
- 1,091
3
votes
A general formula for the number of conjugacy classes of $\mathbb{S}_n \times \mathbb{S}_n$ ...
I discovered this old question in connection with someone else's similar (and current) question: The Simultaneous Conjugacy Problem in the symmetric group $S_N$
If anyone still cares, here is a sligh …
CommunityBot
- 1
5
votes
2
answers
646
views
Decomposing the conjugacy representation of Sym$(n)$ for small $n$
I am trying to compute the decomposition of the conjugacy representation of some small symmetric groups. Perhaps someone has undertaken a similar calculation.
My own calculations are quite slow, eve …
CommunityBot
- 1
1
vote
1
answer
255
views
Groups with no small generating set
Is there a classification of groups having the property that any set of $d$ elements (say including the identity) is contained in a proper subgroup?
It is appealing to call the maximum such integer ( …
- 1,091