We deene noncommutative analogues of the characters of the symmetric group which are induced by transitive cyclic subgroups (cyclic characters). We investigate their properties by means of the formalism of noncommutative symmetric functions. The main result is a multiplication formula whose commutative projection gives a combinatorial formula for the resolution of the Kronecker product of two c...

A (left) group code of length n is a linear code which is the image of a (left) ideal of a group algebra via an isomorphism FG→ F which maps G to the standard basis of F. Many classical linear codes have been shown to be group codes. In this paper we obtain a criterion to decide when a linear code is a group code in terms of its intrinsical properties in the ambient space F, which does not assu...

In this paper we study the connections between cyclic presentations of groups and branched cyclic coverings of (1, 1)-knots. In particular , we prove that every n-fold strongly-cyclic branched covering of a (1, 1)-knot admits a cyclic presentation for the fundamental group encoded by a Heegaard diagram of genus n.

We give a classification of all the countable 1-transitive cyclic orderings, being those on which the automorphism group acts singly transitively. We also classify all the countable 1-transitive coloured cyclic orderings, where these are countable cyclic orderings in which each point is assigned a member of a set C, thought of as its ‘colour’, and by ‘1transitivity’ we now mean that the automor...

We give a characterization for fundamental groups of graphs of groups amalgamating cyclic edge subgroups to be cyclic subgroup separable if each pair of edge subgroups has a non-trivial intersection. We show that fundamental groups of graphs of abelian groups amalgamating cyclic edge subgroups are cyclic subgroup separable, hence residually finite, if each edge subgroup is isolated in its conta...

We determine completely the structure of finite 2-groups which possess exactly six cyclic subgroups of order 4. This is an exceptional case because in a finite 2-group is the number of cyclic subgroups of a given order 2n (n ≥ 2 fixed) divisible by 4 in most cases and this solves a part of a problem stated by Berkovich. In addition, we show that if in a finite 2-group G all cyclic subgroups of ...

The problem of finding minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic groups. This problem was considered earlier by other authors. We give a construction of an undirected graph having 4n+ 6 vertices and automorphism group cyclic of order 4n, n ≥ 1. As a special case we get graphs with 2k + 6 vertices and cyclic automorphism g...

A formula is obtained for the dimension a(n; m) of the space of degree m invariants of the regular representation of the n-th order cyclic group. This formula implies in particular that a(n; m) = a(m; n). Moreover, the automorphism group of the multiplicative semigroup generated by invariant monomials of the cyclic group in that representation is determined.

Plasma and 24-hour urinary cyclic AMP and cyclic GMP levels were determined by saturation analysis in specimens from normal subjects and from 101 patients with tumours of the gastrointestinal tract, breast, lung, bladder or prostate, or with cirrhosis of the liver. Relative to 46 control subjects, plasma cyclic GMP concentrations were significantly elevated in seven patients with gastric tumour...

Garside groups are a natural lattice-theoretic generalisation of the braid and spherical type Artin–Tits groups. Here we show that class is closed under some free products with cyclic amalgamated subgroups. We deduce every tree product infinite group. Moreover, study those HNN extensions as well. Using theorem Pietrowski, conclude this paper by stating non-cyclic one-relator group if only its c...