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2d
comment Periodic group with bound on order of finite subgroups
It is known that finitely generated periodic finitely generated dimensional complex linear groups are finite, which is one reason to expect that the groups asked about will not be straightforward.
Sep
15
comment A p-Sylow of a group $G$ is characteristic in its normalizer $N_G(S)$?
I agree with Venkataramana. The place to start is to consider how many subgroups of order $|S|$ are contained in $N_{G}(S).$
Sep
11
revised Are bounds known for the maximum determinant of a (0,1)-matrix of specified size and with a specifed number of 1s?
added coments
Sep
11
revised Are bounds known for the maximum determinant of a (0,1)-matrix of specified size and with a specifed number of 1s?
typo
Sep
11
revised Are bounds known for the maximum determinant of a (0,1)-matrix of specified size and with a specifed number of 1s?
typo
Sep
11
revised Are bounds known for the maximum determinant of a (0,1)-matrix of specified size and with a specifed number of 1s?
rearranged
Sep
11
revised Are bounds known for the maximum determinant of a (0,1)-matrix of specified size and with a specifed number of 1s?
simplified
Sep
11
answered Are bounds known for the maximum determinant of a (0,1)-matrix of specified size and with a specifed number of 1s?
Sep
10
comment Is there any possibily that we can restore the original sequence from a specific permutation?
On the basis of the information you have given, there is nothing to distinguish between $a_{1}-b_{1}$ and any other $a_{i}- b_{j}.$
Sep
9
comment Integration of gaussian times absolute value of cosine
Can't the first estimate be combined with Cauchy Schwarz? Something like $\int_{0}^{\infty} \exp(-(x/c)^{2})|\cos(x)| dx \leq \sqrt{\int_{0}^{\infty} \exp(-(x/c)^{2})\cos^{2}(x)dx \int_{0}^{\infty} \exp(-(x/c)^{2})}dx$?
Sep
9
comment In what sense is the classification of all finite groups “impossible”?
On reflection, I think there are lots of perfectly valid classifications which give workable characterizations, but could not be implemented in finite time. Jordan normal form over the complex numbers, for example- there are uncountably many Jordan normal forms in each dimension. The classification of finite simple groups requires, strictly speaking, the knowledge of all prime powers. So invoking computational complexity introduces new questions ( which may be good).
Sep
9
comment In what sense is the classification of all finite groups “impossible”?
I think the more precise expression "or parametrizes them" suggests giving a recipe (in terms, say, of a list of invariants) which allows the list to be reconstructed in a systematic way. I think we all agree that group multiplication tables are not the best way to describe groups.
Sep
8
comment In what sense is the classification of all finite groups “impossible”?
I think that a reasonable interpretation of classification is a list which enumerates (or parametrizes them) in such a way that we can be sure that each one is described once and only once.
Sep
8
comment In what sense is the classification of all finite groups “impossible”?
I would not say that the classification of possible Jordan normal forms for $n \times n$ matrices gets conceptually more difficult as $n$ increases: there is a good parametrization of possibilities for any dimension.
Sep
8
comment In what sense is the classification of all finite groups “impossible”?
I am not sure (though others may be) whether there is any realistic hope of enumerating precisely the number of isomorphism types of groups of order $p^{n}$ for general primes $p$ and positive integers $n.$ There are good asymptotic estimates, but knowing the exact number seems to be another matter.
Sep
7
revised What are smallest finite images of triangle groups?
simplified argument
Sep
7
revised What are smallest finite images of triangle groups?
clarified
Sep
7
revised What are smallest finite images of triangle groups?
expanded comments
Sep
7
revised What are smallest finite images of triangle groups?
gave a supply of examples
Sep
7
comment What are smallest finite images of triangle groups?
@DavidLHarden: Yes indeed. My point was just that in seeking the smallest such group, it might be useful to know that in several cases, the group in question is necessarily simple.