G5096 - Algebra - Group Axioms - Flashcards in University Mathematics

It is the axiom which states that a(bc) = (ab)c for all a,b,c ∈ G

Associativity

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For any group G and elements a,b,x ∈ G, one has that ax=ay => x=y

Cancellation Law

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This is a set which follows four axioms: Closure, Associativity, Identity and Inverse

Group

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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

Identity

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It is the axiom which states that every element can under go the binary operation with another element to make the identity element.

Inverse

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A group G where ab=ba for all a,b ∈ G

Abelian

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The number of elements in a group G, sometimes denoted as |G|

Order

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It is the axiom which states there exists a binary operation G x G -> G (eg: (a,b) -> ab)

Closure

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Other cards in this set

For any group G and elements a,b,x ∈ G, one has that ax=ay => x=y

Cancellation Law

This is a set which follows four axioms: Closure, Associativity, Identity and Inverse

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

It is the axiom which states that every element can under go the binary operation with another element to make the identity element.

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