Second lady understanding of the group

In essence, the group = + nonempty binary operation defined group includes four aspects:

1. Closed: binary operation defined to meet this property
2. Associativity: makes sure you get only the results of operations when more than one element, operational impact has not, so there is (or na) expression
3. Identity element: the only
4. Inverse: any element and are the only

Special group is cyclic group;

Group Examples: Z (addition); a Zn (addition)

Clear definition group, we then understand the definition and nature of various types of special subgroups of groups:

Subgroup + H = group subset of the binary operation G; H subgroup may determine a plurality of cosets; | accompany number set | * | H | = | G |

Defined normal subgroup important requirements AH ∈ H, wherein h∈H, a∈G; followed by a quotient group G / H;

NOTE: conjugated concept; automorphism; isomorphism; homomorphism;