The image of the generic point Spec ( K ) → Spec ( R ) → g is contained in O h for v and h are conjugate over K. Since O h is a closed subvariety of g and since Spec ( R ) is irreducible it follows that ϕ v factors through the embedding O h ↪ g. □.
Obviously, all the maximal cliques in G are contained in the set of the resulting cliques.
We may assume that the support of g is contained in the ball (B 0,R)), where R is a positive number.
Note that (mathrm{Rad}_{mathrm{ea}}(G)) is contained in the amenable radical of (G), that appears (but for its name) in [56, Lemma 1 of Section 4].
G possesses a (pi )-Hall subgroup (that is, a subgroup of order (|G|_pi )), every two (pi )-Hall subgroups are conjugate in G, every (pi )-subgroup of G is contained in some (pi )-Hall subgroup.
Remark 15 Under the assumptions that G has closed graph and the values of G are contained in some ball, Theorem 5.1 in [9] states that the problem (1) has robust solutions.
The solid source, GaAs powders (approximately 1.0 g), was contained in a boron nitride crucible, which was then positioned in the upstream zone with a distance of approximately 10 cm away from the substrate with catalysts.
Firstly, if without the pruning operations specified in Lines 9 and 13 of Algorithm 2, all the maximal cliques in G are contained in the set of cliques returned by Algorithm 2.
It is known that (Gin mathscr {D}_pi ) if and only if the complete analog of the Sylow Theorem holds for (pi )-subgroups of G, that is, (1) G possesses a (pi )-Hall subgroup (that is, a subgroup of order (|G|_pi )), (2) every two (pi )-Hall subgroups are conjugate in G, (3) every (pi )-subgroup of G is contained in some (pi )-Hall subgroup.
Informally, a subgroup is a group H contained within a bigger one, G. Concretely, the identity element of G is contained in H, and whenever h1 and h2 are in H, then so are h1 h2 and h1−1, so the elements of H, equipped with the group operation on G restricted to H, indeed form a group.
