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A Group theory. Composition

  1. Jan 27, 2017 #1
    Is it mathematically correct to call any group operation in ##(G,\cdot)## composition?
     
  2. jcsd
  3. Jan 27, 2017 #2

    fresh_42

    Staff: Mentor

    As long as you stay consistent, yes. Usually one wouldn't describe groups like ##\mathbb{Z}## by a dot as binary operator, or a matrix group like ##GL(n)## by an addition, but strictly speaking it doesn't matter which symbol for the operation is used. This changes however, if more than one operation is involved. So you may write ##a \circ b\, , \,a+b\, , \,a \cdot b\, , \,a * b## or simply ##ab##. But you should think about the readability: ##3 \cdot 5 = 8## in ##(\mathbb{Z},+)## might be quite disturbing.
     
  4. Jan 27, 2017 #3
    Thanks. I do not asked about notation but just calling. Is it fine to say that 3+5=8 composition of numbers 3 and 5 is 8
     
  5. Jan 27, 2017 #4

    fresh_42

    Staff: Mentor

    Yes, although composition is used in some other contexts, e.g. composition series. So product or addition sum might be better, but on principle: yes.
     
  6. Jan 27, 2017 #5

    micromass

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    No, I would never call that composition. I have never seen it refered to as composition. Composition should be used for functions mainly.
     
  7. Jan 27, 2017 #6

    fresh_42

    Staff: Mentor

    As this it's at least the operation in ##GL(n)##.
     
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