# Subnormal subgroup

attainable subgroup

Any member of any subnormal series of a group. To indicate the subnormality of a subgroup $H$ in a group $G$, the notation $H \lhd\!\lhd G$ is used.

#### References

 [1] M.I. Kargapolov, J.I. [Yu.I. Merzlyakov] Merzljakov, "Fundamentals of the theory of groups" , Springer (1979) (Translated from Russian)

A subnormal subgroup of $G$ that coincides with its commutator subgroup and whose quotient by its centre is simple is called a component of $G$. The product of all components of $G$ is known as the layer of $G$. It is an important characteristic subgroup of $G$ in the theory of finite simple groups, see e.g. [a1].