Meaning of normal series

nor'mal se'ries

Pronunciation: [key]
— Math. Math.
  1. a collection of subgroups of a given group so arranged that the first subgroup is the identity, the last subgroup is the group itself, and each subgroup is a normal subgroup of the succeeding subgroup.
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.