In 1993, Muzychuk [18] showed that the rational Schur rings over a cyclic group Zn are in one-to-one correspondence with sublattices of the divisor lattice of n, or equivalently, with sublattices of the lattice of subgroups of Zn. This can easily be extended to show that for any finite group G, sublattices of the lattice of characteristic subgroups of G give rise to rational Schur rings over G ...

“High risk” groups for exacerbations of chronic obstructive pulmonary disease (COPD) in the 2011 Global Initiative for Chronic Obstructive Lung Disease (GOLD) proposal (i.e. groups C and D) [1] include: patients with a forced expiratory volume in 1 s FEV1 <50% reference and <2 exacerbations year (subgroups C1 and D1); patients with ⩾2 exacerbations·year and an FEV1 ⩾50% reference (subgroups C2 ...

The Chinese Stenopsyche simplex Group is revised for the first time since Weaver's (1987) revision. The group includes 14 described species and 3 new species. Two diagnostic subgroups were recognized by Schmid (1959). The first subgroup of Chinese species includes S. anaximander Malicky 2011, S. brevata Tian & Zheng 1989, S. chinensis Hwang 1957, S. dentata Navás 1930, S. splendida Martynov 193...

The (.)reg construction was introduced in order to make an arbitrary semigroup S divide a regular semigroup (S)reg which shares some important properties with S (e.g., finiteness, subgroups, torsion bounds, J-order structure). We show that (S)reg can be described by a rather simple complete string rewrite system, as a consequence of which we obtain a new proof of the normal form theorem for (S)...

We show that the stable module $\infty$-category of a finite group $G$ decomposes in three different ways as limit $\infty$-categories certain subgroups $G$. Analogously to Dwyer's terminology for homology decompositions, we call these centraliser, normaliser, and subgroup decompositions. construct centraliser normaliser decompositions extend decomposition (constructed by Mathew) more collectio...

We consider subrings S of rings R such that R = S⊕V with V either two sided invariant under multiplication by S or invariant under the commutator with S. We show that some important properties of R are inherited by S under such conditions. One is the FCR-property which says that every finite dimensional representation is completely reducible. Another application gives a characterization (in cha...