현대대수, 대수학 군(group) 에 관한 논문입니다.
3. cyclic groups
5. normal subgroups
6. factor groups
A group < *> is a set , closed under a binary operation *, such that the following axiom are satisfied:
: For all , we have
****. associativity of *
: There is an element in such that for all
**. identity element for *
: Corresponding to each , there is an
element in such that
**. inverse of
A group is abelian if its binary operation is commutative.
The set Z+ under multiplication is not group. There is an identity 1, but no inverse of 3.
The set of all real-valued functions with domain R under function addition is a group. This group is abelian.
The set Mm×n(R) of all m×n matrices under matrix addition is a group. The m×n matrix with all entries 0 is the identity matrix. This group is abelian.
In group with binary operation *, there is only one element in such that