منابع مشابه
A finite basis theorem for product varieties of groups
It is shown that, if IJ is a subvariety of the join of a nilpotent variety and a metabelian variety and if V̂ is a variety with a finite basis for its laws, then UV also has a finite basis for its laws. The special cases IJ nilpotent and IJ metabelian have been established by Higman (1959) and Ivanjuta (1969) respectively. The proof here, which is independent of Ivanjuta's, depends on a rather g...
متن کاملChow Groups of Some Generically Twisted Flag Varieties
We classify the split simple affine algebraic groups G of types A and C over a field with the property that the Chow group of the quotient variety E/P is torsion-free, where P ⊂ G is a special parabolic subgroup (e.g., a Borel subgroup) and E is a generic G-torsor (over a field extension of the base field). Examples of G include the adjoint groups of type A. Examples of E/P include the Severi-B...
متن کاملSome Abelian Varieties with Visible Shafarevich-Tate Groups
We give examples of abelian variety quotients of the modular jacobian J0(N) with nontrivial visible Shafarevich-Tate groups. In computing these examples we developed formulas for invariants of higher dimensional modular abelian varieties.
متن کاملInaccessible Varieties of Groups
A weak but still unsolved version of the first half of Problem 7 in Hanna Neumann's book [5] asks whether the product 1193 of a nontrivial join-irreducible variety VL and an arbitrary variety 93 is necessarily also join-irreducible. One of the results of this paper is a positive answer provided either It is abelian or the infiniterank free groups of IX have no nontrivial abelian verbal subgroup...
متن کاملSome Applications of Strong Product
Let G and H be graphs. The strong product GH of graphs G and H is the graph with vertex set V(G)V(H) and u=(u1, v1) is adjacent with v= (u2, v2) whenever (v1 = v2 and u1 is adjacent with u2) or (u1 = u2 and v1 is adjacent with v2) or (u1 is adjacent with u2 and v1 is adjacent with v2). In this paper, we first collect the earlier results about strong product and then we present applications of ...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1970
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700045901