Phylogenetic structure of Guinea-Bissau ethnic groups for mitochondrial DNA and Y chromosome genetic systems

The maternal and paternal genetic profile of Guineans is markedly sub-Saharan West African, with the majority of lineages belonging to L0-L3 mtDNA sub-clusters and E3a-M2 and E1-M33 Y chromosome haplogroups. Despite the sociocultural differences among Guinea-Bissau ethnic groups,marked by the supposedly strict admixture barriers, their genetic pool remains largely common. Their extant variation coalesces at distinct timeframes, from the initial occupation of the area to later inputs of people. Signs of recent expansion in mtDNA haplogroups L2a-L2c and NRY E3a-M2 suggest population growth in the equatorial western fringe, possibly supported by an early local agricultural centre, and to which the Mandenka and the Balanta people may relate. Non-West African signatures are traceable in less frequent extant haplogroups, fitting well with the linguistic and historical evidence regarding particular ethnic groups: the Papel and Felupe-Djola people retain traces of their putative East African relatives; U6 and M1b among Guinea-Bissau Bak-speakers indicate partial diffusion to Sahel of North African lineages; U5b1b lineages in Fulbe and Papel represent a link to North African Berbers, emphasizing the great importance of post-glacial expansions; exact matches of R1b-P25 and E3b1-M78 with Europeans likely trace back to the times of the slave trade.

On invariant Rings of Sylow subgroups of finite classical groups

In this thesis we study the invariant rings for the Sylow p-subgroups of the nite classical groups. We have successfully constructed presentations for the invariant rings for the Sylow p-subgroups of the unitary groups GU(3; Fq2) and GU(4; Fq2 ), the symplectic group Sp(4; Fq) and the orthogonal group O+(4; Fq) with q odd. In all cases, we obtained a minimal generating set which is also a SAGBI basis. Moreover, we computed the relations among the generators and showed that the invariant ring for these groups are a complete intersection. This shows that, even though the invariant rings of the Sylow p-subgroups of the general linear group are polynomial, the same is not true for Sylow p-subgroups of general classical groups. We also constructed the generators for the invariant elds for the Sylow p-subgroups of GU(n; Fq2 ), Sp(2n; Fq), O+(2n; Fq), O-(2n + 2; Fq) and O(2n + 1; Fq), for every n and q. This is an important step in order to obtain the generators and relations for the invariant rings of all these groups.