# A Group theory. Composition

1. Jan 27, 2017

### LagrangeEuler

Is it mathematically correct to call any group operation in $(G,\cdot)$ composition?

2. Jan 27, 2017

### 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.

3. Jan 27, 2017

### LagrangeEuler

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

4. Jan 27, 2017

### 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.

5. Jan 27, 2017

### micromass

Staff Emeritus
No, I would never call that composition. I have never seen it refered to as composition. Composition should be used for functions mainly.

6. Jan 27, 2017

### Staff: Mentor

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