Treffer: Crossed homomorphisms from rank-2 abelian to exceptional p-groups: Crossed homomorphisms from rank-2 Abelian to exceptional \(p\)-groups.
Title:
Crossed homomorphisms from rank-2 abelian to exceptional p-groups: Crossed homomorphisms from rank-2 Abelian to exceptional \(p\)-groups.
Authors:
Source:
Journal of Algebra. 270:212-237
Publisher Information:
Elsevier BV, 2003.
Publication Year:
2003
Subject Terms:
Homological methods in group theory, Algebra and Number Theory, Finite nilpotent groups, \(p\)-groups, numbers of crossed homomorphisms, semidihedral groups, dihedral groups, 0101 mathematics, 01 natural sciences, Arithmetic and combinatorial problems involving abstract finite groups, Automorphisms of abstract finite groups
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
Language:
English
ISSN:
0021-8693
DOI:
10.1016/s0021-8693(03)00451-4
Access URL:
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....c3a2ff637d0f45cd5afafd1aa032cc4d
Database:
OpenAIRE
Weitere Informationen
Let \(A\) and \(G\) be finite groups with group homomorphism \(\varphi\colon A\to\Aut(G)\). A map \(\xi\colon A\to G\) is said to be a crossed homomorphism if \(\xi(ab)=\xi(a)\varphi(a)(\xi(b))\). Let \(Z^1(A,G)\) be the set of all crossed homomorphisms from \(A\) to \(G\). \textit{T. Asai} and \textit{T. Yoshida} [J. Algebra 160, No. 1, 273-285 (1993; Zbl 0827.20034)] conjectured that \(|Z^1(A,G)|\equiv 0\pmod{\gcd(|A/[A,A]|,|G|)}\). The authors confirm this conjecture for Abelian groups \(A\) of rank 2 and a group \(G\) which is either a cyclic \(p\)-group or a 2-group of maximal class.