caa a22 4500 606160760 CHVBK 20210128100631.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10468-015-9519-x doi (NATIONALLICENCE)springer-10.1007/s10468-015-9519-x Ghost Numbers of Group Algebras II [Elektronische Daten] [J. Christensen, Gaohong Wang] We study several closely related invariants of the group algebra k G of a finite group. The basic invariant is the ghost number, which measures the failure of the generating hypothesis and involves finding non-trivial composites of maps each of which induces the zero map in Tate cohomology ("ghosts”). The related invariants are the simple ghost number, which considers maps which are stably trivial when composed with any map from a suspension of a simple module, and the strong ghost number, which considers maps which are ghosts after restriction to every subgroup of G. We produce the first computations of the ghost number for non-p-groups, e.g., for the dihedral groups at all primes, as well as many new bounds. We prove that there are close relationships between the three invariants, and make computations of the new invariants for many families of groups. Springer Science+Business Media Dordrecht, 2015 Tate cohomology nationallicence Stable module category nationallicence Generating hypothesis nationallicence Ghost map nationallicence Christensen J. Department of Mathematics, University of Western Ontario, N6A 5B7, London, ON, Canada aut Wang Gaohong Department of Mathematics, University of Western Ontario, N6A 5B7, London, ON, Canada aut Algebras and Representation Theory Springer Netherlands 18/3(2015-06-01), 849-880 1386-923X 18:3<849 2015 18 10468 https://doi.org/10.1007/s10468-015-9519-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-015-9519-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Christensen J. Department of Mathematics, University of Western Ontario, N6A 5B7, London, ON, Canada aut NATIONALLICENCE 700 1- Wang Gaohong Department of Mathematics, University of Western Ontario, N6A 5B7, London, ON, Canada aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/3(2015-06-01), 849-880 1386-923X 18:3<849 2015 18 10468