Normal sub-group

Definition of normal subgroup:

Group H is a subgroup of G, if any of the a∈g, have AH = Ha, then the H is a normal subgroup of G, recorded as h? G.

Examples of normal subgroups:

1. Special linear groups are normal subgroups of general linear groups.

2. Staggered groups are normal subgroups of symmetric groups.

The nature of the normal subgroup:

1. Set h is the normal subgroup of G, K is a subgroup of H, then H is the normal subgroup of K.

Small episode:

Conjugate subgroups:

Set G is a group, g∈g, the shape (a∈g) element becomes the conjugate element of G. If H is a subgroup of G, it is a subgroup of G and becomes a conjugate subgroup of H.

2.H is the normal subgroup of group G when and only if all the conjugate subgroups of H are equal to H.

3. Set H and K as subgroups of group G, then

(1). If H and K are normal subgroups of Group G, the product of H and K is also the normal subgroup of G

(2). If H and K are both normal subgroups of Group G, then H and K are also normal subgroups of G

(3). If H and K are both normal subgroups of group G, and H and K are the intersection of {e}, then HK = KH is established for arbitrary h∈h and arbitrary k∈k

Regular subgroup Exercises:

Normal sub-group