A closed subgroup H of the affine, algebraic group G is called observable if G/H is a quasi-affine algebraic variety. In this paper we define the notion of an observable subgroup of the affine, algebraic monoid M . We prove that a subgroup H of G is observable in M if and only if H is closed in M and there are “enough” H-semiinvariant functions in k[M ]. We show also that a closed, normal subgr...

Suppose p is the generic type of a differential-algebraic jet space to a finite dimensional differential-algebraic variety at a generic point. It is shown that p satisfies a certain strengthening of almost internality to the constants. This strengthening, which was originally called “being Moishezon to the constants” in [9] but is here renamed preserving internality to the constants, is a model...

Let f be a function from a finite field Fp with a prime number p of elements, to Fp. In this article we consider those functions f(X) for which there is a positive integer n > 2 √ p− 1− 11 4 with the property that f(X) , when considered as an element of Fp[X]/(X −X), has degree at most p− 2− n + i, for all i = 1, . . . , n. We prove that every line is incident with at most t − 1 points of the g...

Let G be a commutative algebraic group over Q. Let Γ be a subgroup of G(Q) contained in the union of the compact subgroups of G(Qp). We formulate a guess for the dimension of the closure of Γ in G(Qp), and show that its correctness for certain tori is equivalent to Leopoldt’s conjecture.

Cross-reacting factor IX material (CRM) was immunologically detected in the plasma of 38 normal individuals and 21 out of 22 haemophilia B patients using a rabbit antibody to factor IX. The same reacting material was detected in only nine of these patients using a human antibody. These results indicate that the plasma of the majority of haemophilia B patients contains a protein-lacking biologic...

Let X be a normal projective algebraic variety, G its largest connected automorphism group, and A(G) the Albanese variety of G . We determine the isogeny class of A(G) in terms of the geometry of X . In characteristic 0, we show that the dimension of A(G) is the rank of every maximal trivial direct summand of the tangent sheaf of X . Also, we obtain an optimal bound for the dimension of the lar...

We will say that a smooth projective complex algebraic variety V (of dimension n − 1) is a fake Pn−1 if V is the quotient of the unit ball Bn−1 by a torsion-free cocompact discrete subgroup of PU(n − 1, 1), and all the Betti numbers of V are equal to those of Pn−1 C . If the fundamental goup of a fake P n−1 is an arithmetic subgroup of PU(n − 1, 1), then we will say that it is an arithmetic fak...

For an inclusion F < G < L of connected real algebraic groups such that F is epimorphic in G, we show that any closed F -invariant subset of L/3 is G-invariant, where 3 is a lattice in L. This is a topological analogue of a result due to S. Mozes, that any finite F -invariant measure on L/3 is G-invariant. This result is established by proving the following result. If in addition G is generated...

In this paper, we define the algebraic structures of multi-fuzzy subgroup and some related properties are investigated. The purpose of this study is to implement the fuzzy set theory and group theory in multi-fuzzy subgroups. Characterizations of multi-level subsets of a multi-fuzzy subgroup of a group are given.

In this paper we apply results from algebraic number theory to subgroup separability of linear groups. We then state applications to subgroup separability of free products with amalgamation of hyperbolic 3-manifold groups.