Sentence examples for a proper subgroup of from inspiring English sources

Then (HK_{0}) is a proper subgroup of (G).

and Sp ( N / 2 ) is a proper subgroup of SU ( N ).

In this case, the Weyl group of the associated Lie algebra is isomorphic to a proper subgroup of the isotropy group of the Weyl groupoid.

In view of Z ( G ) ⩽ C G ( x ), one has that Z ( G ) is a proper subgroup of G, and 3, 7 ∉ π ( Z ( G ) ).

Suppose that ((Hbigcap K K_{p^{prime }}) is a proper subgroup of (K) and let (K_{0}) be a maximal subgroup of (K) containing ((Hbigcap K K_{p^{prime }}).

Therefore, F ∗ ( E ) is a proper subgroup of E. (2) Let p be the smallest prime dividing the order of F and P be a Sylow p-subgroup of F.

Moreover, in the last case, (pi _varepsilon ne varnothing ) since otherwise (|H|=2) and H is contained as a proper subgroup in a Sylow 2-subgroup P of S, contrary to Lemma 2.9.

It is a proper subgroup, so that by Proposition 5.5 P ′ contains a copy of G m, R.

Clearly, (mathcal {H}) is a proper subgroup because (r+r^{21} =jOmega.) Let (gamma ) and (gamma ') satisfy (5.2).

A group G is minimal nonsolvable if G is nonsolvable but every proper subgroup of G is solvable.

As in studies with premature neonates, selecting the proper subgroup of patients with ARDS for HFOV treatment will be a main issue in trials comparing HFOV with CV [ 16].