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We assign to each pair of positive integers $n$ and $k \geq 2$ a digraph $G (n, k)$ whose set of vertices is $H = {0, 1, \dots, n - 1}$ and for which there is a directed edge from $a \in H$ to $b \in H$ if $a^{k} \equiv b (mod n)$ . We investigate the structure of $G (n, k)$ . In particular, upper bounds are given for the longest cycle in $G (n, k)$ . We find subdigraphs of $G (n, k)$ , called fundamental constituents of $G (n, k)$ , for which all trees attached to cycle vertices are isomorphic.

The structure of disjoint iteration groups on the circle

Krzysztof Ciepliński (2004)

Czechoslovak Mathematical Journal

The aim of the paper is to investigate the structure of disjoint iteration groups on the unit circle $𝕊^{1}$ , that is, families $ℱ = {F^{v} 𝕊^{1} ⟶ 𝕊^{1} v \in V}$ of homeomorphisms such that $F^{v_{1}} \circ F^{v_{2}} = F^{v_{1} + v_{2}}, v_{1}, v_{2} \in V,$ and each $F^{v}$ either is the identity mapping or has no fixed point ( $(V, +)$ is an arbitrary $2$ -divisible nontrivial (i.e., $c a r d V > 1$ ) abelian group).

The Structure of Ext (A,..) and V = L.

Martin Huber, H.L. Hiller, S. Shelah (1978)

Mathematische Zeitschrift

The structure of finite p-groups: effective proof of the coclass conjectures.

Aner Shalev (1994)

Inventiones mathematicae

The structure of $G$ -free nilpotent groups of step 3.

Amaglobeli, M. (2004)

Georgian Mathematical Journal

The structure of hemigroups.

K.P. Chinda, Jane M. Day (1980)

Aequationes mathematicae

The structure of hemigroups. (Short Communication).

K.P. Chinda, Jane M. Day (1980)

Aequationes mathematicae

The structure of idempotent residuated chains

Wei Chen, Xian Zhong Zhao (2009)

Czechoslovak Mathematical Journal

In this paper we study some special residuated lattices, namely, idempotent residuated chains. After giving some properties of Green’s relation $𝒟$ on the monoid reduct of an idempotent residuated chain, we establish a structure theorem for idempotent residuated chains. As an application, we give necessary and sufficient conditions for a band with an identity to be the monoid reduct of some idempotent residuated chain. Finally, based on the structure theorem for idempotent residuated chains, we obtain...

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The structure of a complete $l$ -group

The structure of bisimple left unipotent semigroups as ordered pairs.

The structure of bisimple orthodox semigroups as ordered pairs.

The structure of certain integrally closed semigroups.

The structure of commutative ideal semigroups.

The structure of digraphs associated with the congruence $x^{k} \equiv y (mod n)$

The structure of disjoint iteration groups on the circle

The Structure of Ext (A,..) and V = L.

The structure of finite p-groups: effective proof of the coclass conjectures.

The structure of $G$ -free nilpotent groups of step 3.

The structure of hemigroups.

The structure of hemigroups. (Short Communication).

The structure of idempotent residuated chains

The structure of left C-rpp semigroups.

The structure of Morita dual monoids.

The structure of orthodox unions of groups.

The structure of P-regular semigroups.

The structure of regular semigroups, I: A representation.

The structure of regular semigroups, II: Cross connections.

The structure of regular semigroups, III: The reduced case.

Currently displaying 581 – 600 of 856