Sentence examples for a normal series from inspiring English sources

Thus 1 ⊴ H ⊴ K ⊴ G is a normal series, as desired.

By Wilson's theorem [11] (hat{G}) possesses a normal series all of whose factors are either p-groups or Cartesian products of isomorphic non-abelian finite simple groups.

By Lemma 2.1, G has a normal series 1 ⊴ N ⊴ G 1 ⊴ G such that N and G / G 1 are π 1 -groups and G 1 / N is a non-abelian simple group, N is a nilpotent group.

Since G is non-solvable, by Lemma 1, we get that G has a normal series 1 ⊴ H ⊴ K ⊴ G such that K / H is a direct product of isomorphic non-abelian simple groups and | G / K | ∣ | Out ( K / H ) |.

Hence H is non-solvable and H has a normal series 1 ⊴ N ⊴ M ⊴ H such that M / N is a direct product of isomorphic non-abelian simple groups and | H / M | ∣ | Out ( M / N ) |.

Then there exists a normal series of H: 1 ⊴ N ⊴ M ⊴ H such that M / N is a direct product of isomorphic non-abelian simple groups and | H / M | ∣ | Out ( M / N ) |.

Bone marrow aspiration from the sternum showed a hypocellular marrow with complete absence of the erythroid series, a normal myeloid series, and megakaryocytes.

Supernumerary: an additional tooth to the normal series [ 31].

Supplemental: an additional tooth to the normal series resembling the tooth with which it is associated [ 32 ].

Dens invaginatus: an invagination of enamel in the crown of the tooth [ 30 ]. Supernumerary: an additional tooth to the normal series [ 31 ].

For a normal away series — lasting two to four games, and thus one to three nights in a hotel — Todd Frazier said he might take a couple of shirts out and place them on hangers.