Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorjcmckeown
    • CommentTimeNov 26th 2012

    Now there is Sylow p-subgroup.


    Is there a compilation, somewhere, of the results “the (obvious) automorphisms of a small 𝔄\mathfrak{A} AA are transitive on AA’s maximal 𝔅\mathfrak{B}s?” The only other example ready in my head is that the maximal tori in a compact Lie group are conjugate, but I know I’ve seen more.

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 26th 2012

    The p-torsion article that is linked to from Sylow p-subgroup seems to refer only to abelian groups (?).

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 26th 2012

    The p-torsion article

    I wasn’t aware of that article. It overlaps a bit with the other article, torsion subgroup. I don’t have time to merge them now, but I have added cross-links. (And I fixed the typo in the definition! :-)

    • CommentRowNumber4.
    • CommentAuthorjcmckeown
    • CommentTimeNov 26th 2012

    @Todd, hmm… see, I was only looking for the proof of the unproved theorem now in Sylow, so I didn’t look too closely… And now I see you’re right, and therefore that the thing in the p-torsion page really should be called simply a prime factor of GG, or at most a Smith submodule — (er, did a Smith really write Smith’s Algorithm?)

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeSep 23rd 2018

    Added a proof of existence of Sylow subgroups mentioned by Benjamin Steinberg at the Café.

    diff, v7, current

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 23rd 2018

    I’m probably being dim but shouldn’t one add a condition to HH. I mean, what’s to stop HH being trivial. Or is that OK, and one can speak of the trivial group as a pp-Sylow subgroup of itself for any pp? Don’t we need positive powers of pp?

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeSep 23rd 2018

    Nothing stops HH from being trivial or of order prime to pp; there the pp-Sylow subgroup is trivial as you surmise.

    • CommentRowNumber8.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 23rd 2018

    There are some people who insist on pp-groups and pp-subgroups being nontrivial, e.g., Steven Roman in Fundamentals of Group Theory, pp. 80-81, but I guess this is just a convention.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)