Yet another Freiheitssatz: Mating finite groups with locally indicable ones

The main result includes as special cases on the one hand, the Gerstenhaber--Rothaus theorem (1962) and its generalisation due to Nitsche and Thom (2022) and, on the other hand, the Brodskii--Howie--Short theorem (1980--1984) generalising Magnus's Freiheitssatz (1930).Comment: 5 pages. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.ht

Equations over solvable groups

Not any nonsingular equation over a metabelian group has solution in a larger metabelian group. However, any nonsingular equation over a solvable group with a subnormal series with abelian torsion-free quotients has a solution in a larger group with a similar subnormal series of the same length (and an analogous fact is valid for systems of equations).Comment: 7 pages. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V3: misprints correcte

The structure, function and evolution of a complete human chromosome 8

The complete assembly of each human chromosome is essential for understanding human biology and evolution(1,)(2). Here we use complementary long-read sequencing technologies to complete the linear assembly of human chromosome 8. Our assembly resolves the sequence of five previously long-standing gaps, including a 2.08-Mb centromeric alpha-satellite array, a 644-kb copy number polymorphism in the beta-defensin gene cluster that is important for disease risk, and an 863-kb variable number tandem repeat at chromosome 8q21.2 that can function as a neocentromere. We show that the centromeric alpha-satellite array is generally methylated except for a 73-kb hypomethylated region of diverse higher-order alpha-satellites enriched with CENP-A nucleosomes, consistent with the location of the kinetochore. In addition, we confirm the overall organization and methylation pattern of the centromere in a diploid human genome. Using a dual long-read sequencing approach, we complete high-quality draft assemblies of the orthologous centromere from chromosome 8 in chimpanzee, orangutan and macaque to reconstruct its evolutionary history. Comparative and phylogenetic analyses show that the higher-order alpha-satellite structure evolved in the great ape ancestor with a layered symmetry, in which more ancient higher-order repeats locate peripherally to monomeric alpha-satellites. We estimate that the mutation rate of centromeric satellite DNA is accelerated by more than 2.2-fold compared to the unique portions of the genome, and this acceleration extends into the flanking sequence

The complete sequence of a human genome.

Since its initial release in 2000, the human reference genome has covered only the euchromatic fraction of the genome, leaving important heterochromatic regions unfinished. Addressing the remaining 8% of the genome, the Telomere-to-Telomere (T2T) Consortium presents a complete 3.055 billion-base pair sequence of a human genome, T2T-CHM13, that includes gapless assemblies for all chromosomes except Y, corrects errors in the prior references, and introduces nearly 200 million base pairs of sequence containing 1956 gene predictions, 99 of which are predicted to be protein coding. The completed regions include all centromeric satellite arrays, recent segmental duplications, and the short arms of all five acrocentric chromosomes, unlocking these complex regions of the genome to variational and functional studies

The complete sequence of a human genome.

Since its initial release in 2000, the human reference genome has covered only the euchromatic fraction of the genome, leaving important heterochromatic regions unfinished. Addressing the remaining 8% of the genome, the Telomere-to-Telomere (T2T) Consortium presents a complete 3.055 billion-base pair sequence of a human genome, T2T-CHM13, that includes gapless assemblies for all chromosomes except Y, corrects errors in the prior references, and introduces nearly 200 million base pairs of sequence containing 1956 gene predictions, 99 of which are predicted to be protein coding. The completed regions include all centromeric satellite arrays, recent segmental duplications, and the short arms of all five acrocentric chromosomes, unlocking these complex regions of the genome to variational and functional studies