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Russ Woodroofe's user avatar
Russ Woodroofe's user avatar
Russ Woodroofe
  • Member for 13 years
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Generating random finite groups
It's not clear to me that the procedure described above wouldn't favor certain isomorphism classes. The original question wanted an equal chance at each isomorphism class of groups of order $n$.
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Generating random finite groups
Indeed, GAP even knows the count of these groups with NumberSmallGroups (but it won't let you get at the groups themselves via the SmallGroups library).
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Generating random finite groups
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Is there a (satisfying) proof that cellular cohomology is isomorphic to simplicial cohomology that doesn't use relative cohomlogy?
awarded
 Necromancer
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Making spheres shellable
Is the difference with the Adiprasito and Benedetti theorem in the nature of the allowed subdivisions? They only look at derived subdivisions.
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Making spheres shellable
awarded
 Yearling
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Flag complexes that are shellable but not vertex decomposable
awarded
 Autobiographer
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Generalization of a theorem of Øystein Ore in group theory
There's also Roland Schmidt's nice book "Subgroup lattices of groups", which goes into a bit more depth on most of these and many related topics.
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The Wedge Sum of path connected topological spaces
Link to amazon webpage for Hilton and Wylie is here: amazon.com/Homology-Theory-Introduction-Algebraic-Topology/d‌​p/…
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quasiprimitive non-solvable groups
John, that link looks wustl.edu specific. Try ams.org/mathscinet-getitem?mr=2661653 instead. (And no mathscinet access is required for that link.)
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Factor subsets of a finite group
@Geoff Robinson: Yes, sounds like a good place to look for a possible counterexample.
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Characterising extendable automorphisms
See also this related question mathoverflow.net/questions/7782/…
revised
Characterising extendable automorphisms
commented on difficulty of problem; other minor edits
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Characterising extendable automorphisms
The groupprops wiki has a couple of articles regarding this, e.g. groupprops.subwiki.org/wiki/Extensible_automorphisms_problem . While I found these to be rather incomplete, they give a start in finding some references.
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Characterising extendable automorphisms
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When is $S_n \times S_m$ a subgroup of $S_p$?
It's maybe worth pointing out that 6! / (5! \cdot 3!) is an integer (is 1), so you can't rule this out purely from the index of the subgroup.
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Sylow 3-subgroups of symmetric group
See also en.wikipedia.org/wiki/Symmetric_group#Sylow_subgroups
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