The relationship between free groups and graphs is one of the many examples of the interaction between seemingly foreign branches of mathematics. After defining and proving elementary relations between graphs and groups, this paper will present a result of Hanna Neumann on the intersection of free subgroups. Although Neumann’s orginal upper bound on the rank of the intersection has been improve...

1.1 Notation. As Bourbaki intended, we let N denote the set of finite cardinals, {0, 1, 2, . . .}. Throughout this section, let F be a field. We shall write dim(V ) to denote the F-dimension of an F-module V . Throughout this section, let (Z,VZ,EZ,EZ ι,τ −→ VZ) be a finite (oriented) graph; here, Z is a finite set, VZ ⊆ Z, EZ = Z −VZ, and ι and τ are functions. Each e ∈ EZ has an associated pic...

The aim of this paper is to try and outline the activities Hanna Szumańska-Wertheim in Warsaw during 1943–1944 period. It provides information about arrest her husband, Stanisław Wertheim, underground cultural undertakings (the “Wisła” publishing house). author also draws readers’ attention Szumańska-Wertheim’s as a courier resistance movement.

Article Marcus Coelen/Oliver Precht/Hanna Sohns (Hgg.), Pessoa denken. Eine Einführung. Mit Texten von und zu Fernando Pessoa, Wien, Turia + Kant, 2020. 244 Seiten. was published on November 8, 2022 in the journal Romanistisches Jahrbuch (volume 73, issue 1).

The Friedman--Mineyev theorem, earlier known as the (strengthened) Hanna Neumann conjecture, gives a sharp estimate for rank of intersection two subgroups in free group. We obtain an analogue this inequality any virtually group (or, more generally, containing product left-orderable groups finite-index subgroup).