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In previous work, we introduced the notion of binomial cup-one algebras, which are differential graded algebras endowed with Steenrod $\cup_1$-products and compatible binomial operations. Given such an $R$-dga, $(A,d_A)$, defined over the ring $R=\mathbb{Z}$ or $\mathbb{Z}_p$ (for $p$ a prime), with $H^0(A)=R$ and with $H^1(A)$ a finitely generated, free $R$-module, we show that $A$ admits a functorially defined 1-minimal model, $\rho\colon (\mathcal{M}(A),d)\to (A,d_A)$, which is unique up to isomorphism. Furthermore, we associate to this model a pronilpotent group, $G(A)$, which only depends on the 1-quasi-isomorphism type of $A$. These constructions, which refine classical notions from rational homotopy theory, allow us to distinguish spaces with isomorphic (torsion-free) cohomology rings that share the same rational 1-minimal model, yet whose integral 1-minimal models are not isomorphic., Comment: 74 pages

Motivated by the construction of Steenrod cup-$i$ products in the singular cochain algebra of a space and in the algebra of non-commutative differential forms, we define a category of binomial cup-one differential graded algebras over the integers and over prime fields of positive characteristic. The Steenrod and Hirsch identities bind the cup-product, the cup-one product, and the differential in a package that we further enhance with a binomial ring structure arising from a ring of integer-valued rational polynomials. This structure allows us to define the free binomial cup-one differential graded algebra generated by a set and derive its basic properties. It also provides the context for defining restricted triple Massey products, which have a smaller indeterminacy than the classical ones, and hence, give stronger homotopy type invariants., Comment: 45 pages; accepted for publication in Topology and its Applications

We explore finitely generated groups by studying the nilpotent towers and the various Lie algebras attached to such groups. Our main goal is to relate an isomorphism extension problem in the Postnikov tower to the existence of certain commuting diagrams. This recasts a result of G. Rybnikov in a more general framework and leads to an application to hyperplane arrangements, whereby we show that all the nilpotent quotients of a decomposable arrangement group are combinatorially determined., Comment: 34 pages; accepted for publication in the European Journal of Mathematics

The objectives of this study were to: (a) identify those attitudes which best serve to explain the concept of teacher militancy, and (b) provide a basis for development of concise instruments for the assessment of such attitudes. A survey instrument, entitled "Classroom Teacher Point of View," was constructed to assess attitudes of teachers regarding their work environments and regarding issues commonly associated with teacher militancy, union organization, and professionalization. The self-administering survey instruments were returned by 2,178 classroom teachers in elementary and secondary schools in the 1,389 California unified school districts which had an average daily attendance greater than 4,000. Results of the survey provided a basis for defining teacher militancy as a complex of attitudes characteristically including (a) pronounced lack of confidence in school district administration, (b) general lack of support for the school principal, (c) cynical disbelief in the integrity of those in authority, (d) dissatisfaction with existing conditions of education, (e) strong predisposition toward educational change in general, (f) marked tendency to accept the processes of union organization, and (g) inclination to seek increased professional authority and responsibility. (Author/MJM)