Semantic evolution of the word “Law”

The article uncovers the semantic history of the word “law”. In ancient Russian manuscripts the word “law” combined both secular and religious meanings. Semantic structure of the word “law” broadened based on its meanings, used in natural and social sciences. Specialization of this word in jurisprudence facilitated the use of the term “law” for stipulating a normative act. Semantic evolution of the word “law” lead to broadening the area of its usage. Key words: law, custom, inner form of a word, norm, limit, jurisprudence, evolution, semantic structure of a word

Conjugation-invariant norms on the commutator subgroup of the infinite braid group

In this paper, we give another proof of the result of Brandenbursky and Kȩdra which says that the commutator subgroup of the infinite braid group admits stably unbounded norms. Moreover, we observe that the norms which we construct are equivalent to the bi-invariant word norm studied by Brandenbursky and Kȩdra.

THE CANCELLATION NORM AND THE GEOMETRY OF BI-INVARIANT WORD METRICS

We study bi-invariant word metrics on groups. We provide an efficient algorithm for computing the bi-invariant word norm on a finitely generated free group and we construct an isometric embedding of a locally compact tree into the bi-invariant Cayley graph of a nonabelian free group. We investigate the geometry of cyclic subgroups. We observe that in many classes of groups, cyclic subgroups are either bounded or detected by homogeneous quasimorphisms. We call this property the bq-dichotomy and we prove it for many classes of groups of geometric origin.