IJPAM: Volume 35, No. 3 (2007)

ANOTHER CHARACTERIZATION FOR
A CERTAIN INVARIANT FOR A GROUP PAIR

Maria Gorete Carreira Andrade$^1$, Ermínia de Lourdes Campello Fanti$^2$,
Flávia Souza Machado da Silva$^3$
$^{1,2,3}$Department of Mathematics - IBILCE
UNESP - São Paulo State University
R. Cristovão Colombo, 2265
15064-000 - São José do Rio Preto, SP, BRAZIL
$^1$e-mail: gorete@ibilce.unesp.br
$^2$e-mail: fanti@ibilce.unesp.br
$^3$e-mail: flaviasmsilva@bol.com.br


Abstract.In this paper we show some examples about the relations of the quotient $\frac{ H^1(G,S;M)} {P(G,S,M)} $ with splittings of a split extension and we give another characterization for the invariant $\widetilde{E}(G,S):=1+\text{\rm dim}_{\Z_{2}}\ \text{\rm Ker}\,(\text{\rm res}\,^{G}_{S,{\cal F}_{S}G})$ studied in [#!jan!#] for $(G:S)= \infty$. With this characterization we can extend the definition of $\widetilde{E}(G,S)$ for the case $(G:S)< \infty$.

Received: December 22, 2006

AMS Subject Classification: 20J06, 55M05, 20E06

Key Words and Phrases: relative cohomology of groups, extension of groups, ends of pairs of groups

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 35
Issue: 3