G5096 - Algebra - Group Axioms
- Created by: callumdavidwatts
- Created on: 02-01-17 23:43
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Clues
- A group G where ab=ba for all a,b ∈ G (7)
- For any group G and elements a,b,x ∈ G, one has that ax=ay => x=y (12, 3)
- It is the axiom which states that a(bc) = (ab)c for all a,b,c ∈ G (13)
- It is the axiom which states that every element can under go the binary operation with another element to make the identity element. (7)
- It is the axiom which states that there is a element I which when under the binary operation with another element a the result will be a (8)
- It is the axiom which states there exists a binary operation G x G -> G (eg: (a,b) -> ab) (7)
- The number of elements in a group G, sometimes denoted as |G| (5)
- This is a set which follows four axioms: Closure, Associativity, Identity and Inverse (5)
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