Hygrophorus sect. Olivaceoumbrini: new boundaries, extended biogeography and unexpected diversity unravelled by transatlantic studies

As currently delineated, Hygrophorus sect. Olivaceoumbrini is a polyphyletic assembly within subg. Colorati, encompassing glutinous and pigmented taxa. According to available literature, between a dozen and twenty species may belong in the section, mostly represented in continental and boreal forests of Europe and North America. However, the limited phylogenetic and biogeographic coverage of the genus does not presently allow for a reliable assessment of its taxonomic boundaries, nor does it provide a complete picture of species diversity within sect. Olivaceoumbrini. In an ongoing effort to confer an evolutionary backbone to Hygrophorus systematics, we assembled and analysed a dataset comprising 268 intercontinental sequences, including holotypes of 7 taxa previously not positioned phylogenetically, and enriched with collections from largely unexplored Mediterranean and Anatolian ecosystems. Overall, 30 clades are identified within 5 distinct lineages, including 11 species putatively new to science. Seven of these are formally described here as H. agathosmoides, H. albofloccosus, H. canadensis, H. limosus, H. marcocontui, H. pinophilus and H. pustulatoides spp. nov. This enriched coverage of section Olivaceoumbrini s.lat. calls for a re-evaluation of its natural boundaries into a core monophyletic clade, including H. olivaceoalbus and five closely related lookalikes, as well as the assignment of the section rank to the four remaining lineages: sect. Fuscocinerei sect. nov., sect. Limacini sect. nov., sect. Nudolidi sect. nov. and sect. Tephroleuci, respectively. We also stabilize the usage of six historical names, H. glutinifer, H. hyacinthinus, H. mesotephrus, H. olivaceoalbus, H. pustulatus and H. tephroleucus, through designation of two neotypes, three lectotypes and four epitypes.

On the Diagnostic Role of Morphological Signs of Wild Rose (Rosa L.)

Identification and systematics of species of wild rose (Rosa L.) are often associated with difficulties due to the diversity and variability of morphological features used in this process. They also arise in establishing genetic links between taxa of different ranks. Clarity in the diagnostic role of specific or group of characters is not only theoretical but also of practical importance. Such an attempt is made on the example of species of the genus Rosa from different sections and subsections (R. canina. R. danaiorum, R. ruprechtii, R. marschalliana, R. obtusifolia, R. svanetica, Rosa mollis, R. buschiana, R. pulverulenta, R pomifera, R. iberica, R. pimpinnefolia, etc.) of Chechnya and adjacent territories. The set of signs of the vegetative and generative sphere used in identifying species, subsections, sections has been considered. There was a lack of representativeness for the intraspecific diagnostics of such signs as: “free, immersed columns”, or “sessile stigmas in the hemispherical head above the fetal throat”, “occasionally solid sepals, with downward directed fruits” and others used in sectional diagnoses, because they are characteristic of species of different sections. The authors noted the heterogeneity of the authors’ approach to the characterization of section rank taxa, the inadmissibility of the universal, and the need for a differentiated approach in using the same characteristics when identifying taxa of different levels.

‘COHOMOLOGY AND PROFINITE TOPOLOGIES FOR SOLVABLE GROUPS OF FINITE RANK’

We remedy an omission in the proof of Proposition 2.7 of the paper ‘Cohomology and profinite topologies for solvable groups of finite rank’, Bull. Aust. Math. Soc.86 (2012), 254–265. This proposition states that a solvable group with finite abelian section rank has merely finitely many subgroups of any given index.

GROUPS IN WHICH THE NORMAL CLOSURES OF CYCLIC SUBGROUPS HAVE FINITE SECTION RANK

A group G is said to have finite section p-rankrp(G) = r (here p is a prime) if every elementary abelian p-section U/V of G is finite of order at most pr and there is an elementary abelian p-section A/B of G such that |A/B| = pr. If ℙ is the set of all primes and λ : ℙ → ℕ ∪ {0} is a function, we say that a group G has λ-bounded section rank if rp(G) ≤ λ(p) for each p ∈ ℙ. In this paper we show that if G is a locally generalized radical group in which the normal closures of the cyclic subgroups of G have finite λ-bounded section rank, then [G,G] has [Formula: see text]-bounded section rank for some function [Formula: see text]. This is a wide generalization of some results by Neumann, Smith and many others. Moreover we are able to give explicit formulas for the involved bounds.

SOME CRITERIA FOR EXISTENCE OF SUPPLEMENTS TO NORMAL SUBGROUPS AND THEIR APPLICATIONS

We established several new criteria for existence of complements and supplements to some normal abelian subgroups in groups. In passing, as one of the many useful applications and corollaries of these results, we obtained a description of some finitely generated soluble groups of finite Hirsch–Zaitsev rank. As another application of our results, we obtained a D.J.S. Robinson's theorem on structure of finitely generated soluble groups of finite section rank. The original proof of this theorem was homological, but all proofs in this paper, including this one, are purely group-theoretical.

On Hyper (Abelian of Finite Rank) Groups

We study the class of groups G, each of whose non-trivial images contains a non-trivial abelian normal subgroup of finite rank. This is very much wider than the class, studied earlier by Robinson and others, of hyperabelian groups H with finite abelian section rank. Our main results are that these groups G are hypercentral by residually finite and are divisible by hypo(abelian of finite exponent). They need not be divisible by residually finite, unlike the groups H above. In practice, we work with a somewhat wider but less easily described class of groups.