The most of the previous work on the complexity of in nite words has measured the complexity as descriptional one, i. e. an in nite word w had a \small" complexity if it was generated by a morphism or another simple machinery, and w has been considered to be \complex" if one needs to use more complex devices (gsm's) to generate it. In [J. Hromkovi c, J. Karhum aki, A. Lepist o: \Comparing des...

1.1 Graded associative algebras. A nite Z-grading of an algebra A is a decomposition A = L n i=?n A i such that A i A j A i+j , where A i = 0 for jij > n. From now on a grading means a nite Z-grading. I am interested in associative graded algebras because they arise naturally in study of Lie algebras, although the subject is certainly interesting in its own right. A classiication of gradings of...

About 60 years ago H. Zassenhaus 17] classiied nite near-elds. In doing so he also gave a full description of those nite groups which have a representation D (over C) such that D(g) has no eigenvalue 1 for any nontrivial element g 2 G. In our terminology such a group is called semiregular. One of the results in 17] characterizes SL 2 (5) as the only perfect semiregular group. Clearly, if the un...

Various forms of the extension problem are discussed for linear codes de ned over nite rings. The extension theorem for symmetrized weight compositions over nite Frobenius rings is proved. As a consequence, an extension theorem for weight functions over certain nite commutative rings is also proved. The proofs make use of the linear independence of characters as well as the linear independence ...