Ronald C. Brown

Minimal covers of S n by Abelian subgroups and maximal subsets of pairwise noncommuting elements

Abstract We give best possible asymptotic upper and lower bounds for the minimal cardinality βn of a cover of the symmetric group Sn by abelian subgroups and the maximal cardinality αn of a set of pairwise noncommuting elements of Sn. We show that the average values of β n (n − 2) ! and of α n (n − 2) ! are bounded above and below by positive constants. Finally, we show that the sequence { β n α n } is bounded and that if it converges, then βn = αn for all n⩾0.

Abelian Frobenius kernels and modules over number rings

Some categories of groups (typically involving groups, possibly infinite, with abelian Frobenius kernels) are shown to be equivalent to categories whose objects are modules over groups and rings. The rings in question are associated with algebraic number fields, and the category equivalences allow some applications of number theory to group theory. In particular the number of isomorphism classes of metabelian Frobenius groups with kernel of order n and complement of order m is calculated in terms of the prime factorization of n and the structure of the Euler group (ZmZ)•.

Roots of Irreducible Polynomials in Tame Henselian Extension Fields

A class of irreducible polynomials 𝒫 over a valued field (F, v) is introduced, which is the set of all monic irreducible polynomials over F when (F, v) is maximally complete. A “best-possible” criterion is given for when the existence of an approximate root in a tamely ramified Henselian extension K of F of a polynomial f in 𝒫 guarantees the existence of an exact root of f in K.

FTAs in Asia-Pacific: "Next Generation" of Social Dimension Provisions on Labor?

FTAs in Asia-Pacific: “Next Generation�? of Social Dimension Provisions on Labor? Recent years have brought a proliferation of Free Trade Agreements (“FTA�?), bilateral and multilateral, often regional, with even larger ones being negotiated, such as the European Union (“EU�?) and United States (“U.S.�?) Transatlantic Trade and Investment Partnership (TTIP) and the Transpacific Partnership (TPP). The Asia Pacific Economic Cooperation (“APEC�?) forum members recently discussed plans to “phase out regional free trade agreements�? (or supplement them) in favor of creating a singular Free Trade Agreement Asia Pacific (“FTAAP�?), covering much of the Asia Pacific Region. While inter-Asian business grows and FTAs flourish in and with Asia, the inclusion of social dimension provisions in FTAs or Bilateral Investment Treaties (“BIT�?) is practically non-existent, except where the Western influence appears to dominate, and social dimension provisions are included, such as in FTAs with South Korea and with Singapore. The thesis of this paper is straightforward; there are workers throughout the world, particularly in developing countries, who are subjected to substandard labor standards, and their countries are targeted for investment because of their countries’ low wages or lax enforcement of labor laws. The existence of domestic labor laws and ratification of ILO Core Labor Conventions do not necessarily provide labor protection for the workers. Likewise, international treaty obligations under FTAs with social dimension provisions on labor do not necessarily bring labor protections. There are a number of emerging FTAs in the Pacific Region and the several very significant ones on the cusps of conclusion are discussed below so as to evaluate current approaches of labor protections by FTAs. This paper proposes the “new generation�? of FTA social dimension provisions should embrace a marriage of international obligations, which incorporate mandates for private contractual remedies under International Framework agreements (“IFA�?), CSRs, and Codes of Conduct, with the private obligations contractually enforceable by private parties.

THE MAIN INVARIANT OF A DEFECTLESS POLYNOMIAL

In an earlier paper the authors calculated the main invariant of a tame polynomial over a valued field in terms of the simple invariants associated with a strict system of polynomial extensions that contained that polynomial. In this note we give upper and lower bounds in terms of such invariants for the main invariant of any defectless polynomial. We also determine precisely the polynomials for which the upper bound is the main invariant; this class strictly contains the set of tame polynomials. A class of examples with the same upper and with the same lower bound for the main invariant is given whose main invariants form a dense subset of the interval between the two bounds. A second class of polynomials is given whose strict systems have arbitrarily long length and whose main invariant is the lower bound. A basic tool is a formula for the main invariant which itself gives an algorithm for computing the main invariants of the polynomials in any strict system; in particular, simple formulas are given for the main invariants of some very special types of defectless polynomials including generalized Schonemann polynomials. The Krasner constants of defectless polynomials are also studied.

The Space of Real Places on R(x,y)

Abstract The space M(ℝ (x; y)) of real places on ℝ (x; y) is shown to be path-connected. The possible value groups of these real places are determined and for each one it is shown that the set of real places with that value group is dense in the space. Large collections of subspaces of the space M(ℝ (x; y)) are constructed such that any two members of such a collection are homeomorphic. A key tool is a homeomorphism between the space of real places on ℝ((x))(y) and a certain space of sequences related to the “signatures” of [2], which themselves are shown here to be related to the “strict systems of polynomial extensions” of [3].

U.S.-Russia-East Asia Comparisons of Dispatch (Temporary) Worker Regulations

Russia had few temporary workers in the 1990s, but after the fall of the Soviet Union and the entrance of foreign MNCs, the percent of workers on temporary contracts grew in 2014. In 2016, a new law was implemented that bans hiring temporary workers except through government-accredited agencies, but only for the purpose of substituting for employees who are temporarily absent from the workplace; to assist in the temporary expansion of production or services (for up to a maximum of nine months); and to provide temporary employment to certain approved categories of workers (i.e., fulltime students, single parents, parents of multiple children, and former convicts). This paper will compare and contrast the current labor protections of temporary dispatch workers in the U.S. and Russia, with consideration also of the recent legislative labor protections provided in the East Asian countries of China, South Korea, and Japan. Following the Introduction, the paper, in Part I discusses the phenomena of “fissurization,” in employment relations and its resulting legal implications for the regulation of “dispatch (agency)” workers in the above countries. Part II compares and contrasts the regulatory approaches of the U.S. with Russia and the East Asian countries of China, Japan, and South Korea; and the Conclusion follows. Perhaps the menu of regulatory legislation provided in this paper will be useful for those looking for the tools to construct dispatch regulation in the U.S.

China – U.S. Implementation of ILO Standards by BITs and Pieces (FTAs)

Implementing ILO standards can be complex and requires analysis in different dimensions. This paper approaches that issue from assessing whether and how international obligations may affect implementation of ILO core labour standards. Distinguishing between the levels of obligation generated from commitment to the ILO Declaration versus a core labour standard Convention is important as the international instruments of Bilateral Investment Treaties and Free Trade Agreements may use either or both. Discussion explores the nature of the obligations as they may differ. The international vehicles employing labour obligations are found in BITs and FTAs and can be found in U.S. instruments, but are usually absent in China’s FTAs. Obligations can range from commitments to ratify Conventions to not derogating from existing labour legislation and with varying enforcement mechanisms. Currently, the U.S. and China are negotiating a BIT in which the U.S. Model BIT contains obligations relating to the ILO core labour standards. The influence or the obligations of these international undertakings on the national standards resulting from implementation are the theme of this paper. Also, briefly presented is a description of current labour legislation in the U.S. and in China and the existing gaps in the requirements of the ILO core labour standards were they to be implemented, in the event there is an appetite to obligate and reduce the gaps.