Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    ReputationRep:
    Name:  111.PNG
Views: 71
Size:  172.8 KB


    I tried to highlight the bit of terminology I don't understand and give some context to this.

    The bits I don't get are mainly the "action" (unless I'm getting it correct below as a guess of what I think it could mean) and "(element wise) stabilisers" and "stabilisers", if anyone could explain these I would be grateful as I don't see what it means.

    In this particular case we are talking about a group of automorphisms acting on a set of elements of a field. I believe the "action" of G on the field is just applying an element of G (an automorphism) to a element of the field. (Is this correct?) The group here is the Galois group of some arbitrary field extension L/K and the field it acts on is L.

    But I have no idea what the highlighted paragraph means in particular I have never come across the term elementwise stabiliser? Could it mean the set of all automorphisms of G that map each element of {u1,...,uk} into {u1,...,uk} i.e. some kind of permutation on these k elements? Or is it something else entirely?

    I will answer any questions if I haven't been clear enough in due course.
    • Thread Starter
    Offline

    0
    ReputationRep:
    EDIT: I believe I understand now. Set-wise is the set of all automorphisms in Gal(L/K) that map {u1,...,uk} into the set {u1,...,uk} and element-wise is the set of all automorphisms in Gal(L/K) that map each ui in {u1,...,uk} to itself.
    • Thread Starter
    Offline

    0
    ReputationRep:
    In particular I think the highlighted bit is the set

    \displaystyle \{\Phi \in \text{Gal}(L/K): \Phi (u_i)=u_i ~\forall i=1,2,...,k\}

    any confirmation on this would be nice though.
    Offline

    18
    ReputationRep:
    (Original post by matthew69238)
    Any confirmation on this would be nice though.
    Yes.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Brussels sprouts
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.