On a new product of groups
type: Item
instance of: scholarly article
title: On a new product of groups
zbMATH Open document ID: 0797.05051
published in: European Journal of Combinatorics
publication date: 1994-10-10T00:00:00Z
review text: A new product of groups, the rotary product, is introduced: Let \(G\) be a group, Sym\((G)\) the group of all permutations on \(G\) and Sym\(_ e(G)\) the stabilizer of the identity \(e\in G\) in Sym\((G)\). A subgroup \(H\) of Sym\(_ e(G)\) is called rotary closed provided that \(L_{\phi(g)^{- 1}}\phi L_ g\psi\in H\) for all \(\phi,\psi\in H\) and \(g\in G\), where \(L_{\phi(g)^{-1}}\), \(L_ g\in\text{Sym}(G)\) are left multiplications by the elements \(\phi(g)^{-1}\) and \(g\), respectively. For a group \(G\) and a rotary closed subgroup \(H\) of Sym\(_ e(G)\) the rotary product \(G\odot H\) is defined to be the set \(G\times H\) together with the multiplication \((g,\phi)\cdot(f,\psi)=(g\cdot\phi(f),\phi\odot_ g\psi)\).
reviewed by: Ulrike Baumann
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 597750
zbMATH Keywords: product of groups
zbMATH Keywords: rotary product
author: Robert Jajcay
MaRDI profile type: Publication
full work available at URL: eujc.1994.1027
OpenAlex ID: W1974224901
DOI: 10.1006/EUJC.1994.1027
description: scientific article; zbMATH DE number 597750