Our recent estimates of galaxy counts and the luminosity density in the near-infrared (Keenan et al. 2010, 2012) indicated that the local universe may be under-dense on radial scales of several hundred megaparsecs. Such a large-scale local under-density could introduce significant biases in the measurement and interpretation of cosmological observables, such as the inferred effects of dark energy on the rate of expansion. In Keenan et al. (2013), we measured the K-band luminosity density as a function of distance from us to test for such a local under-density. We made this measurement over the redshift range 0.01 < z < 0.2 (radial distances D ~ 50 - 800 h 70 −1 Mpc). We found that the shape of the K-band luminosity function is relatively constant as a function of distance and environment. We derive a local (z < 0.07, D < 300 h 70 −1 Mpc) K-band luminosity density that agrees well with previously published studies. At z > 0.07, we measure an increasing luminosity density that by z ~ 0.1 rises to a value of ~ 1.5 times higher than that measured locally. This implies that the stellar mass density follows a similar trend. Assuming that the underlying dark matter distribution is traced by this luminous matter, this suggests that the local mass density may be lower than the global mass density of the universe at an amplitude and on a scale that is sufficient to introduce significant biases into the measurement of basic cosmological observables. At least one study has shown that an under-density of roughly this amplitude and scale could resolve the apparent tension between direct local measurements of the Hubble constant and those inferred by Planck team. Other theoretical studies have concluded that such an under-density could account for what looks like an accelerating expansion, even when no dark energy is present.

A detailed investigation was conducted to identify the main factors influencing the current poor reproductive performance in dairy herds in Northern Ireland. Nineteen herds were selected and a comprehensive database was established, comprising detailed information collected over a 2-year period. Milk progesterone monitoring (no.=1423 cows), based on twice weekly sampling, was included in this on-farm investigation. The mean interval from calving to commencement of luteal activity was 30·1 days and 13·4% (184/1378) of these cows had not commenced luteal activity by day 50 post partum. In addition, there was a high incidence of abnormal progesterone profiles: delayed ovulation type I; 15·6% (242/1388), delayed ovulation type II; 11·7% (125/965), persistent corpus luteum type I; 19·4% (212/1121) and persistent corpus luteum type II; 11·9% (70/619). Delayed commencement of luteal activity and abnormal profiles were associated with reduced fertility performance manifested as increased interval to first AI service and ultimately prolonged calving interval. Delayed commencement of luteal activity and abnormal progesterone profiles, with the exception of ‘delayed ovulation type II’ profiles, were not associated with lower conception rates. Assistance at calving was associated with delayed commencement of luteal activity. Delayed commencement of luteal activity and delayed ovulation types I and II profiles were associated with indicators of nutritional stress and poorer production performance in early lactation. Retained foetal membranes were strongly associated with prolonged luteal phases (persistent corpus luteum types I and II profiles). While hormonal therapy may prove useful in treating cows with abnormal milk progesterone profiles, the prevention and treatment of associated diseases and the implementation of good management practices are likely to be more rewarding.

For n a positive integer, a group G is called core-n if H/HG has order at most n for every subgroup H of G (where HG is the normal core of H, the largest normal subgroup of G contained in H). It is proved that a locally finite core-n group G has an abelian subgroup whose index in G is bounded in terms of n.

A group G has all of its subgroups normal-by-finite if H / coreG(H) is finite for all subgroups H of G. These groups can be quite complicated in general, as is seen from the so-called Tarski groups. However, the locally finite groups of this type are shown to be abelian-by-finite; and they are then boundedly core-finite, that is to say, there is a bound depending on G only for the indices | H: coreG(H)|.

We consider the generalisation from central series to marginal series in groups and set up firstly various basic results. The main section of the paper is concerned with the study of which group theoretical properties may be transferred from a marginal factor in a group to the corresponding verbal subgroup and which properties may be transferred from one factor of a lower marginal series to successive factors of the series.

We recall from (3) that a group G is (centrally) eremitic if there exists a positive integer e such that, whenever an element of G has some power in a centralizer, it has its eth power. The eccentricity of an eremitic group G is the least such positive integer e.

In ((4), Theorem A) we proved that if A is a torsion free Abelian normal subgroup of a finitely generated group G with G/A nilpotent, then G has a subgroup of finite index with eccentricity 1. In this note we use a much simpler method to prove a stronger result.

Let be a class and p a property of groups. We say that p is a bigenetic property of p-groups (or more simply, p is bigenetic in p-groups) if an p-group G has the property p whenever all two-generator subgroups of G have p.