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 کاملOn the Exponent of Triple Tensor Product of p-Groups
The non-abelian tensor product of groups which has its origins in algebraic K-theory as well as inhomotopy theory, was introduced by Brown and Loday in 1987. Group theoretical aspects of non-abelian tensor products have been studied extensively. In particular, some studies focused on the relationship between the exponent of a group and exponent of its tensor square. On the other hand, com...
متن کاملOn Varieties of Groups without Positive Laws
We give negative answers to three questions concerning positive laws and ApA varieties. Let A denote the variety of all abelian groups and Ap — the variety of all abelian groups of exponent p. By F we denote a free group and by V — a verbal subgroup in F . We write G ⊇ F to say that G contains a free nonabelian subsemigroup. A variety generated by G is denoted by var(G). A law u(x1, ..., xn) = ...
متن کاملOn connected automorphism groups of algebraic varieties
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...
متن کاملOn Non-cross Varieties of Groups
Our title has become something of a misnomer, however we retain it since drafts of this note have been quoted with it. Unless otherwise stated our terminology and notation follow that in Hanna Neumann's book [12]. The Oates-Powell Theorem ([12] p. 151) allows us to say that a variety is Cross if and only if it can be generated by a finite group, and to assert that the laws of a Cross variety ar...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1971
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700047110