R. E. Hummel. Electronic Properties of Materials. An Introduction for Engineers. Springer‐Verlag, Berlin – Heidelberg – New York – Tokyo 1985, 319 pages, 219 figures, 30 tables, DM 116.–, ISBN 3‐540‐15631‐3 Springer‐Verlag Berlin – Heidelberg – New York – Tokyo, ISBN 0‐387‐15631‐3 Springer‐Verlag New York – Berlin – Heidelberg – Tokyo

Abstract

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Finite groups whose maximal subgroups have the hall property

“…We use the standard notation and definitions that can be found in [1,6,13,14,20]. Describing the structure of a finite group, we use the notation from [3].…”

“…The variety generated by a group G is the least variety containing G. If an identity holds in G then it holds in every group in the variety generated by G. In particular, every group in the variety generated by a group of exponent m is a periodic group of period m. Necessary information on varieties of groups can be found in [13,20]. …”

A theory of concepts and their combinations II: A Hilbert space representation

“…In this article we present a numerical mathematical model for the representation of a concept, built with a mathematical formalism originally used in quantum mechanics, and we show that the data of the above mentioned experiment can be reproduced by the model. Specifically, the model is built using the Hilbert space of quantum mechanics, states are represented by unit vectors of this Hilbert space and contexts and properties by projection operators, and the change of state under the influence of a context is described by von Neumann's 'quantum collapse state transformation' in Hilbert space [14].…”

Some finite solvable groups with non-trivial lattice endomorphisms

“…Then let P be a relatively free p-group of exponent p, rank n and class c. So P' -<3>(P) and |P : $(P)| = p n . Moreover, given a p'-automorphism of P/P', it can be lifted to an automorphism t) of P of the same order ( [8]). Let Q = (rj) and suppose that Q has order q m , where m > 1 and q is a prime different from p. Assume that Vi = P/P' is a faithful irreducible Q-module, so that F p n is a splitting field over F p of the polynomial x qm -1.…”