Ω-群的同态定理

Homomorphism theory of Ω-group

对Ω-群作了初步的探讨.通过对一般抽象群的同态定理的研究,得到了Ω-群的子群对应定理.设π是Ω-群G与它的商群G/N之间的自然同态,则π建立了G中所有包含N的Ω-子群与G/N中全部Ω-子群之间的一个一一对应.

The Ω-groups are disscussed. Now there are perfect results about the homomorphism theories of abstract groups, through which can achieve the homomorphism theories of Ω-groups. Set π is a natural homomorphism of Ω-group G, then π generats a one-to-one correspondence from all Ω-subgroups in G which contain N to Ω-subgroups in G/N.