A countably compact free Abelian group of size continuum that admits a non-trivial convergent sequence

We show that it is consistent with ZFC that the free Abelian group of cardinality c admits a topological group topology that makes it countably compact with a non-trivial convergent sequence. (C) 2011 Elsevier B.V. All rights reserved.

Almost p-compact groups

We show that if p is a selective ultrafilter, then for each cardinal alpha <= omega(1), there exists a topological group G such that G(beta) is almost p-compact (in particular, countably compact), for beta < alpha, but G(alpha) is not countably compact. If in addition, we assume Martin's Axiom, then the result above holds for every alpha < c. (C) 2012 Elsevier By. All rights reserved.

Capuchin monkey tool use: Overview and implications

Nutcracking capuchins are mentioned in reports dating as far back as the sixteenth century,(1,2) as well as in Brazilian folklore.(3) However, it was barely a decade ago that primatologists ""discovered"" the spontaneous use of stones to crack nuts in a semi-free ranging group of tufted capuchin monkeys. Since then, we have found several more capuchin populations in savanna-like environments which(5-7) employ this form of tool use. The evidence so far only weakly supports geneti cally based behavioral differences between populations and does not suggest that dietary pressures in poor environments are proximate determinants of the likelihood of tool use. Instead, tool use within these capuchin populations seems to be a behavioral tradition that is socially learned and is primarily associated with more terrestrial habits. However, differences in the diversity of ""tool kits"" between populations remain to be understood.

EXTENSION OF AUTOMORPHISMS OF SUBGROUPS

Let G be a group such that, for any subgroup H of G, every automorphism of H can be extended to an automorphism of G. Such a group G is said to be of injective type. The finite abelian groups of injective type are precisely the quasi-injective groups. We prove that a finite non-abelian group G of injective type has even order. If, furthermore, G is also quasi-injective, then we prove that G = K x B, with B a quasi-injective abelian group of odd order and either K = Q(8) (the quaternion group of order 8) or K = Dih(A), a dihedral group on a quasi-injective abelian group A of odd order coprime with the order of B. We give a description of the supersoluble finite groups of injective type whose Sylow 2-subgroup are abelian showing that these groups are, in general, not quasi-injective. In particular, the characterisation of such groups is reduced to that of finite 2-groups that are of injective type. We give several restrictions on the latter. We also show that the alternating group A(5) is of injective type but that the binary icosahedral group SL(2, 5) is not.

Axioms for the coincidence index of maps between manifolds of the same dimension

We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in Z circle plus Z(2). We also show in each setting that the group of values for the index (either Z or Z circle plus Z(2)) is determined by the axioms. Finally, for the general case of coincidence theory for arbitrary pairs of maps between two manifolds we provide a set of axioms which characterize the local Reidemeister trace which is an element of an abelian group which depends on the pair of functions. These results extend known results for coincidences between orientable differentiable manifolds. (C) 2012 Elsevier B.V. All rights reserved.

Food Competition in a Semi-Free-Ranging Cebus apella Group

The competitive regime faced by individuals is fundamental to modelling the evolution of social organization. In this paper, we assess the relative importance of contest and scramble food competition on the social dynamics of a provisioned semi-free-ranging Cebus apella group (n=18). Individuals competed directly for provisioned and clumped foods. Effects of indirect competition were apparent with individuals foraging in different areas and with increased group dispersion during periods of low food abundance. We suggest that both forms of competition can act simultaneously and to some extent synergistically in their influence on social dynamics; the combination of social and ecological opportunities for competition and how those opportunities are exploited both influence the nature of the relationships within social groups of primates and underlie the evolved social structure. Copyright (c) 2008 S. Karger AG, Basel

FREE GROUP ALGEBRAS IN DIVISION RINGS

Let k be an algebraically closed field of characteristic zero and let L be an algebraic function field over k. Let sigma : L -> L be a k-automorphism of infinite order, and let D be the skew field of fractions of the skew polynomial ring L[t; sigma]. We show that D contains the group algebra kF of the free group F of rank 2.

Does group size matter? Cheating and cooperation in Brazilian school children

Cooperation between individuals is an important requisite for the maintenance of social relationships. The purpose of this study was to investigate cooperation in children in the school environment, where individuals could cooperate or not with their classmates in a public goods game. We investigated which of the following variables influenced cooperation in children: sex, group size, and information on the number of sessions. Group size was the only factor to significantly affect cooperation, with small-group children cooperating significantly more than those in large groups. Both sex and information had no effect on cooperation. We suggest that these results reflect the fact that, in small groups, individuals were more efficient in controlling and retaliating theirs peers than in large groups. (C) 2008 Elsevier Inc. All rights reserved.

COMMUTATIVE AUTOMORPHIC LOOPS OF ORDER p(3)

A loop is said to be automorphic if its inner mappings are automorphisms. For a prime p, denote by A(p) the class of all 2-generated commutative automorphic loops Q possessing a central subloop Z congruent to Z(p) such that Q/Z congruent to Z(p) x Z(p). Upon describing the free 2-generated nilpotent class two commutative automorphic loop and the free 2-generated nilpotent class two commutative automorphic p-loop F-p in the variety of loops whose elements have order dividing p(2) and whose associators have order dividing p, we show that every loop of A(p) is a quotient of F-p by a central subloop of order p(3). The automorphism group of F-p induces an action of GL(2)(p) on the three-dimensional subspaces of Z(F-p) congruent to (Z(p))(4). The orbits of this action are in one-to-one correspondence with the isomorphism classes of loops from A(p). We describe the orbits, and hence we classify the loops of A(p) up to isomorphism. It is known that every commutative automorphic p-loop is nilpotent when p is odd, and that there is a unique commutative automorphic loop of order 8 with trivial center. Knowing A(p) up to isomorphism, we easily obtain a classification of commutative automorphic loops of order p(3). There are precisely seven commutative automorphic loops of order p(3) for every prime p, including the three abelian groups of order p(3).

A NOTE ON OPEN 3-MANIFOLDS SUPPORTING FOLIATIONS BY PLANES

We show that if N, an open connected n-manifold with finitely generated fundamental group, is C-2 foliated by closed planes, then pi(1)(N) is a free group. This implies that if pi(1)(N) has an abelian subgroup of rank greater than one, then F has at least a nonclosed leaf. Next, we show that if N is three dimensional with fundamental group abelian of rank greater than one, then N is homeomorphic to T-2 x R. Furthermore, in this case we give a complete description of the foliation.

THE STRUCTURE OF FREE AUTOMORPHIC MOUFANG LOOPS

We describe the structure of a free loop of rank n in the variety of automorphic Moufang loops as a subdirect product of a free group and a free commutative Moufang loop, both of rank n. In particular, the variety of automorphic Moufang loops is the join of the variety of groups and the variety of commutative Moufang loops.

A SURVEY ON FREE OBJECTS IN DIVISION RINGS AND IN DIVISION RINGS WITH AN INVOLUTION

Let D be a division ring with center k, and let D-dagger be its multiplicative group. We investigate the existence of free groups in D-dagger, and free algebras and free group algebras in D. We also go through the case when D has an involution * and consider the existence of free symmetric and unitary pairs in D-dagger.

ScPdZn and ScPtZn with YAlGe type structure: group-subgroup relation and 45Sc solid state NMR spectroscopy

The intermetallic compounds ScPdZn and ScPtZn were prepared from the elements by high-frequency melting in sealed tantalum ampoules. Both structures were refined from single crystal X-ray diffractometer data: YAlGe type, Cmcm, a = 429.53(8), b = 907.7(1), c = 527.86(1) pm, wR2 = 0.0375, 231 F2 values, for ScPdZn and a = 425.3(1), b = 918.4(2), c = 523.3(1) pm, wR2 = 0.0399, 213 F2 values for ScPtZn with 14 variables per refinement. The structures are orthorhombically distorted variants of the AlB2 type. The scandium and palladium (platinum atoms) build up ordered networks Sc3Pd3 and Sc3Pt3 (boron networks) which are slightly shifted with respect to each other. These networks are penetrated by chains of zinc atoms (262 pm in ScPtZn) which correspond to the aluminum positions, i.e. Zn(ScPd) and Zn(ScPt). The corresponding group-subgroup scheme and the differences in chemical bonding with respect to other AlB2-derived REPdZn and REPtZn compounds are discussed. 45Sc solid state NMR spectra confirm the single crystallographic scandium sites. From electronic band structure calculations the two compounds are found metallic with free electron like behavior at the Fermi level. A larger cohesive energy for ScPtZn suggests a more strongly bonded intermetallic than ScPdZn. Electron localization and overlap population analyses identify the largest bonding for scandium with the transition metal (Pd, Pt).