The Infertility Trap: The Fertility Costs of Group-Living in Mammalian Social Evolution

Mammal social groups vary considerably in size from single individuals to very large herds. In some taxa, these groups are extremely stable, with at least some individuals being members of the same group throughout their lives; in other taxa, groups are unstable, with membership changing by the day. We argue that this variability in grouping patterns reflects a tradeoff between group size as a solution to environmental demands and the costs created by stress-induced infertility (creating an infertility trap). These costs are so steep that, all else equal, they will limit group size in mammals to ∼15 individuals. A species will only be able to live in larger groups if it evolves strategies that mitigate these costs. We suggest that mammals have opted for one of two solutions. One option (fission-fusion herding) is low cost but high risk; the other (bonded social groups) is risk-averse, but costly in terms of cognitive requirements.

Limit group invariants for non-free Cantor actions

A Cantor action is a minimal equicontinuous action of a countably generated group $G$ on a Cantor space $X$ . Such actions are also called generalized odometers in the literature. In this work, we introduce two new conjugacy invariants for Cantor actions, the stabilizer limit group and the centralizer limit group. An action is wild if the stabilizer limit group is an increasing sequence of stabilizer groups without bound and otherwise is said to be stable if this group chain is bounded. For Cantor actions by a finitely generated group $G$ , we prove that stable actions satisfy a rigidity principle and furthermore show that the wild property is an invariant of the continuous orbit equivalence class of the action. A Cantor action is said to be dynamically wild if it is wild and the centralizer limit group is a proper subgroup of the stabilizer limit group. This property is also a conjugacy invariant and we show that a Cantor action with a non-Hausdorff element must be dynamically wild. We then give examples of wild Cantor actions with non-Hausdorff elements, using recursive methods from geometric group theory to define actions on the boundaries of trees.

CRACK STRENGTH OF HOLLOW CORE SLABS: EXPERIMENTAL RESEARCH

Introduction. The paper presents the results of research that allow assessing the degree of influence of pre-organized cracks on the character crack formation and on the process of the hollow-core slabs’ deformation under short-term load action.Materials and methods. The hollow-core slabs are made without prestressing – one by traditional technology, the second with pre-organized cracks in the manufacturing process. Physical experiment performed on fall-scale structure of hollow-core slabs of П66.10-81500СП. The authors conducted the tests to the calculated breaking load. Moreover, the authors presented the contrastive analysis of character crack formation and of the hollow-core slabs’ deformation of П66.10-8А500СП traditional manufacturing and with pre-organized cracks.Results. As a result, the authors confirmed the earlier hypotheses about the greater rigidity of plates with pre-organized cracks in comparison with the plates where the cracks arose stochastically and under operational load. The installation of organized cracks did not reduce the bearing capacity, thus, reduced the deformability. Therefore, the width of the crack became smaller and the deflections became less.Discussion and conclusions. In the structures of long length, which are rejected by the second limit group, the organization of cracks at the manufacturing stage allows not putting additional reinforcement to reduce the width and deflection of the crack.

Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings

The objective of this series is to study metric geometric properties of disjoint unions of Cayley graphs of amenable groups by group properties of the Cayley accumulation points in the space of marked groups. In this Part II, we prove that a disjoint union admits a fibred coarse embedding into a Hilbert space (as a disjoint union) if and only if the Cayley boundary of the sequence in the space of marked groups is uniformly a-T-menable. We furthermore extend this result to ones with other target spaces. By combining our main results with constructions of Osajda and Arzhantseva–Osajda, we construct two systems of markings of a certain sequence of finite groups with two opposite extreme behaviors of the resulting two disjoint unions: With respect to one marking, the space has property A. On the other hand, with respect to the other, the space does not admit fibred coarse embeddings into Banach spaces with non-trivial type (for instance, uniformly convex Banach spaces) or Hadamard manifolds; the Cayley limit group is, furthermore, non-exact.

Normal subgroups in limit groups of prime index

Motivated by their study of pro-plimit groups, D. H. Kochloukova and P. A. Zalesskii formulated in [15, Remark after Theorem 3.3] a question concerning the minimum number of generators{d(N)}of a normal subgroupNof prime indexpin a non-abelian limit groupG(see Question*). It is shown that the analogous question for the rational rank has an affirmative answer (see Theorem A). From this result one may conclude that the original question of Kochloukova and Zalesskii has an affirmative answer if the abelianization{G^{\mathrm{ab}}}ofGis torsion free and{d(G)=d(G^{\mathrm{ab}})}(see Corollary B), or ifGis a special kind of one-relator group (see Theorem D).

From local to global conjugacy of subgroups of relatively hyperbolic groups

Suppose that a finitely generated group [Formula: see text] is hyperbolic relative to a collection of subgroups [Formula: see text]. Let [Formula: see text] be subgroups of [Formula: see text] such that [Formula: see text] is relatively quasiconvex with respect to [Formula: see text] and [Formula: see text] is not parabolic. Suppose that [Formula: see text] is elementwise conjugate into [Formula: see text]. Then there exists a finite index subgroup of [Formula: see text] which is conjugate into [Formula: see text]. The minimal length of the conjugator can be estimated. In the case, where [Formula: see text] is a limit group, it is sufficient to assume only that [Formula: see text] is a finitely generated and [Formula: see text] is an arbitrary subgroup of [Formula: see text].

Pro-p completions of groups of cohomological dimension 2

We study when an abstract finitely presented group [Formula: see text] of cohomological dimension [Formula: see text] has pro-[Formula: see text] completion [Formula: see text] of cohomological dimension [Formula: see text]. Furthermore, we prove that for a tree hyperbolic limit group [Formula: see text] we have [Formula: see text] and show an example of a hyperbolic limit group [Formula: see text] that is not free and [Formula: see text] is free pro-[Formula: see text]. For a finitely generated residually free group [Formula: see text] that is not a limit group, we show that [Formula: see text] is not free pro-[Formula: see text].