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comment $2$-group with two isomorphic normal subgroups of index $4$ with non-isomorphic quotients
I'm not sure I understand your example. Could you maybe be more explicit? (Keep in mind that I am only considering finite groups.)
Apr
14
awarded  Yearling
Apr
14
awarded  Student
Apr
14
asked $2$-group with two isomorphic normal subgroups of index $4$ with non-isomorphic quotients
Mar
26
comment Max order for which connected Cayley Graphs are known to be Hamiltonian
It has been checked to 1280 that, in the cubic vertex-transitive case, only the four well-known exceptions occur. The question asked for Cayley graphs of arbitrary valency.
Mar
21
answered Max order for which connected Cayley Graphs are known to be Hamiltonian
Feb
24
comment On the Groups of Order $(p^2+1)/2$
ADDENDUM: there are three more candidates for $p$ between 3 and 4 million: $p=3319597,3456127,3636443$, and then none up to 10 million.
Feb
24
comment On the Groups of Order $(p^2+1)/2$
A small observation : since the group has odd order, it is soluble. In particular, it has SOME (minimal) abelian normal subgroup. Moreover, by "Groups of Cube-Free Odd Order", by Curran, we may assume that the group is not cube-free. Anyway, I checked the conjecture up to $p=3000000$. I was only checking that $n=(p^2+1)/2$ was not squarefree and that Sylow's theorem would not force a normal $q$-Sylow subgroup of order at most $q^2$ for some prime $q$. Up to $p=3000000$, the only exceptions are for $p=239$, when we get n=$13^4$ and $p=2905807$ when we get $n=5^4∗13∗61∗97∗137∗641$.
Jan
23
answered Upper bound on the number of vertex transitive graphs
Nov
15
answered Fantastic properties of Z/2Z
Sep
15
revised Presentation of the Monster Group
deleted 344 characters in body
Sep
15
answered Presentation of the Monster Group
Jul
17
comment Maximum automorphism group for a 3-connected cubic graph
In the cubic vertex-transitive case and n twice an odd number, it immediately follows from the same paper that you get a polynomial rather than exponential upper bound. For example Corollary 4 yields that, for large enough n, we have |G|<n^2. This is not best possible, but is not far off, at least for some values of n. If you need more precise estimates, I can show you a few more references that deal with this. (By the way, the link in your "added" section has a typo.)
Jul
17
comment Maximum automorphism group for a 3-connected cubic graph
The family of vertex-transitive graphs you have in mind are in fact best possible among large enough cubic vertex-transitive graphs. (n=100 or so should already suffice.) This is shown in the paper : "Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs", arxiv.org/abs/1010.2546. Therefore, a counter-example to your conjecture will necessarily be not vertex-transitive.
May
26
comment frobenius group
Actually, the Wikipedia page answers both queries (it gives more examples and mentions the odd dihedral groups) and also point towards the fact that being a semidirect product is not enough. It's clear that the author has not even glanced at that page and I would close this question as not being research level.
May
26
comment frobenius group
en.wikipedia.org/wiki/Frobenius_group Not all semidirect products are Frobenius.
Mar
29
awarded  Citizen Patrol
Mar
25
awarded  Yearling
Mar
21
comment Smallest non-isomorphic strongly regular graphs
The links appear to be broken. In the meantime, win.tue.nl/~aeb/graphs/srg/srgtab.html has some information.