𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Note on the Combinatorics of Multiplication in Groups

✍ Scribed by A. Juhász; A. Leibman

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
111 KB
Volume
19
Category
Article
ISSN
0195-6698

No coin nor oath required. For personal study only.

✦ Synopsis

Let S be a finite subset of a group G, |S| = n, and let g ∈ S • S. Then g induces a partial function λ g : S → S by λ g (s) = t if and only if st = g and λ g (s) is not defined if g ∈ sS. For every g ∈ S • S, λ g is a one-to-one mapping. In this note we describe the groups which have a finite generating set S with the property that λ g is a partial permutation for every g ∈ S • S. By a partial permutation we mean a partial function which, when reduced to its domain of definition it becomes a permutation.

📜 SIMILAR VOLUMES

On the Complexity of Some Problems on Gr
On the Complexity of Some Problems on Groups Input as Multiplication Tables
✍ David Mix Barrington; Peter Kadau; Klaus-Jörn Lange; Pierre McKenzie 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 131 KB

The Cayley group membership problem (CGM) is to input a groupoid (binary algebra) G given as a multiplication table, a subset X of G, and an element t of G and to determine whether t can be expressed as a product of elements of X. For general groupoids CGM is P-complete, and for associative algebras

A Note on the Multiplicities of Gorenste
A Note on the Multiplicities of Gorenstein Algebras
✍ Hema Srinivasan 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 167 KB

In this note we give a formula for the multiplicities of homogenous Gorenstein algebras. Herzog, Huneke, and Srinivasan have conjectured bounds for the multiplicities of homogeneous Cohen᎐Macaulay algebras. Herzog and Srinivasan have proved this conjecture for C-M algebras with quasi-pure resolution

A note on groups of colour preserving au
A note on groups of colour preserving automorphisms
✍ Ulrike Baumann; Ute Holthaus 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 233 KB

## Abstract A perfect edge colouring of a graph is defined by the property that all colour matchings are perfect matchings. Every edge‐coloured graph determines a group of graph automorphisms which preserve the colours of the edges. If the graph is connected, then this group of colour preserving au