北京邮电大学 离散数学下 群论 作业错题讲解(14)

北京邮电大学离散数学群论作业详解

群论9.5 (1)4、18、29、30@353-354,

29: Prove H is normal subgroup if H only two left coset.

let a?H, The left cosets of H are H and aH.

The right coset are H and Ha.

H?aH = ?= H?Ha. and H?aH=G=H?Ha.

Thus aH=Ha.

let b∈H, bH=H=Hb. so ?x∈G, xH=Hx.

H is a normal subgroup.