On some theorem of S. Saks

Some Results on Baer's Theorem

Baer has shown that, for a group G, finiteness of G=Zi(G) implies finiteness of ɣi+1(G). In this paper we will show that the converse is true provided that G=Zi(G) is finitely generated. In particular, when G is a finite nilpotent group we show that |G=Zi(G)| divides |ɣi+1(G)|d′ i(G), where d′i(G) =(d( G /Zi(G)))i.

Some Remarks on Kuzmin ' s Theorem for F - Expansions

In this paper a general K d n theorem for a class of multidimensional F-expansions is given. This result gives the uniform rate at which a certain sequence of approximates converges to the density of the invariant measure associated with an F-expansion. Some metric theorems are also given. This work extends and corrects some earlier results. The Jacobi algorithm is included as an example.

Unconditional convergence and the Vitali-Hahn-Saks theorem

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On Kruskal ’ S Theorem

In the first part of this paper, we consider 3 × 3 × 3 arrays with complex entries, and provide a complete self-contained proof of Kruskal’s theorem that the maximum rank is 5. In the second part, we provide a complete classification of the canonical forms of 3× 3× 3 arrays over F2; in particular, we obtain explicit examples of such arrays with rank 6. In 1989, Kruskal [6, page 10] stated witho...

A GENERALIZATION OF SOME GENERALIZATIONS OF SPERNER ' S THEOREM l