Treffer: An Extension Theorem for Euler Characteristics of Groups: An extension theorem for Euler characteristics of groups

Title:
An Extension Theorem for Euler Characteristics of Groups: An extension theorem for Euler characteristics of groups
Authors:
John R. Stallings
Source:
Geometriae Dedicata. 92:3-39
Publisher Information:
Springer Science and Business Media LLC, 2002.
Publication Year:
2002
Subject Terms:
Homological methods in group theory, group extensions, homological algebra, Chain complexes (category-theoretic aspects), dg categories, rational Euler characteristic, 0101 mathematics, Homological dimension (category-theoretic aspects), 01 natural sciences
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
1572-9168
0046-5755
DOI:
10.1023/a:1019696726402
Access URL:
https://zbmath.org/1802402
https://doi.org/10.1023/a:1019696726402
https://link.springer.com/article/10.1023/A%3A1019696726402
Rights:
Springer Nature TDM
Accession Number:
edsair.doi.dedup.....aa32d7d00a669432dedcef8a01ebbe00
Database:
OpenAIRE

Weitere Informationen

Several authors have defined the notion of Euler characteristic of a group, for various classes of groups. Taking the definition due to \textit{I. M. Chiswell} [Math. Z. 147, 1-11 (1976; Zbl 0304.20022)], this paper proves that if \(N\) is a normal subgroup of \(G\) and the Euler characteristics of \(N\), \(G\) and \(G/N\) are defined, then they satisfy the multiplicative property \(\mu(G)=\mu(N)\cdot\mu(G/N)\). See also the preceding review Zbl 1020.20034.