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Questions tagged [gr.group-theory]

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46 votes
12 answers
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Applications of representation theory of the symmetric group

Inspired by this question and in particular the final paragraph of Or's answer, I have the following question: Do you know of any applications of the representation theory of the symmetric group in ...
Sasho Nikolov's user avatar
4 votes
1 answer
152 views

Some nuances on Group and Subgroup Isomorphism?

(1) Is it known Group Isomorphism is in $\mathsf{coNP}$ and is the conjecture so? Is there a good reference for $\mathsf{coNP}$-ness in similar situations? (2) Is subgroup isomorphism $\mathsf{NP\...
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12 votes
1 answer
1k views

What is the hardest instance for the group isomorphism problem?

Two groups $(G,\cdot)$ and $(H, \times)$ are said to be isomorphic iff there exists a homomorphism from $G$ to $H$ which is bijective. The group isomorphism problem is as follows: given two groups, ...
adc's user avatar
  • 177
2 votes
0 answers
139 views

Extending the notion of independence

Background I was looking for a formulation of 'free sets' and 'independent sets' from linear algebra that would extend to groups. This question was considered here but I couldn't find a satisfactory ...
NisaiVloot's user avatar
  • 1,292
-2 votes
1 answer
418 views

Are Graph and Group Isomorphism problems random self-reducible?

Are Graph and Group Isomorphism problems known to be random self-reducible? If so is there a good proof? Are there other non-trivial examples of random self-reducibility? Is there a good reference?
Turbo's user avatar
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