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Feb
3
comment Which non-abelian finite groups have the property that every subgroup is normal?
Yes, these are called Hamiltonian groups and all have the form $Q_8\times A\times B$, where $A$ is an elementary abelian $2$-group, and $B$ is an abelian group of odd order. Here is a link.
Jan
21
comment Number of groups of order $9261$?
@Peter I agree, but ... RTFM? :-) The first paragraph of documentation for this function fairly clearly describes its behaviour. I'm sure the package authors had their reasons for making this design choice. (See, for example, p. 9 of the manual.)
Jan
21
comment Number of groups of order $9261$?
@Peter Please note that my answer does not suggest any error in the ConstructAllGroups command, but rather with how it is used.
Jan
21
comment Number of groups of order $9261$?
@AlexanderKonovalov Thanks for your comment, and for improving my answer formatting.
Jan
21
answered Number of groups of order $9261$?
Jan
16
comment When is every group of order $n$ nilpotent of class $\leq c$?
@FrancisBegbie Yes, I've added a link to a reference.
Jan
16
revised When is every group of order $n$ nilpotent of class $\leq c$?
Added reference.
Jan
16
answered When is every group of order $n$ nilpotent of class $\leq c$?
Jan
6
comment Groups of order $64$ with abelian group of automorphism
@pGroups Right. I forgot to simplify the other presentation.
Jan
4
comment Is $gnu(2304)$ known?
@AlexanderKonovalov Yes, I checked and that is indeed the source for that particular value.
Jan
4
comment Is $gnu(2304)$ known?
According to Maple, $\operatorname{gnu}( 2304 ) = 15756130$. However, Maple does not know $\operatorname{gnu}( 3072 )$.
Dec
29
revised Groups of order $64$ with abelian group of automorphism
Added requested presentations.
Dec
29
revised Groups of order $64$ with abelian group of automorphism
added 4 characters in body
Dec
29
answered Groups of order $64$ with abelian group of automorphism
Dec
14
answered Is there an infinite group that has finite subgroup with finite index?
Dec
1
comment Where can I find the known values for the number-of-groups-function upto $10,000\ $?
It's my understanding that some sort of formula or description is known, but I do not know it! I've never been able to get my hands on the papers where it is described.
Dec
1
comment Where can I find the known values for the number-of-groups-function upto $10,000\ $?
There isn't any general formula or algorithm known for computing the number of groups of a given order $n$, other than to construct all of them. Maple uses formulas for certain special cases, depending on the factorisation of $n$ (for instance, for square-free $n$, or for small powers of primes, etc.) and uses a table of known values for small $n<50000$. I expect GAP and Magma have something similar, but I don't know that PARI has that kind of functionality.
Nov
30
comment Is there a number $n$, such that there are $22$ groups of order $n$?
@Peter I did check for $N(n) = n$ but, for the known values with $2 < n < 50000$, there were none.
Nov
27
answered Is there a number $n$, such that there are $22$ groups of order $n$?