Jo, Jang Hyun On groups of type \(\mathcal L^{-1}\). (English) Zbl 1227.20046 Int. J. Math. 21, No. 6, 727-736 (2010). The author introduces, for a group, certain algebraic properties: “type \(\mathcal L\)” and “type \(\mathcal L^{-1}\)”, and he proves that finite groups (resp. groups of finite virtual cohomological dimension) are of type “\(\mathcal L\)” and “\(\mathcal L^{-1}\)”. He also explains the relation between these results and the work of H. Kawai [Osaka J. Math. 27, No. 4, 937-945 (1990; Zbl 0732.20002)]. Reviewer: Saïd Zarati (Tunis) MSC: 20J06 Cohomology of groups 57S25 Groups acting on specific manifolds 20C20 Modular representations and characters 20C07 Group rings of infinite groups and their modules (group-theoretic aspects) 57M07 Topological methods in group theory Keywords:virtual cohomological dimension; projective resolutions; cohomology of groups; cohomology rings Citations:Zbl 0732.20002 PDFBibTeX XMLCite \textit{J. H. Jo}, Int. J. Math. 21, No. 6, 727--736 (2010; Zbl 1227.20046) Full Text: DOI References: [1] DOI: 10.1006/jabr.1996.6996 · Zbl 0886.20002 [2] Benson D. J., Cambridge Studies in Advanced Mathematics 31, in: Representations and Cohomology. I Cohomology of Groups and Modules (1998) [3] Benson D. J., Cambridge Studies in Advanced Mathematics 31, in: Representations and Cohomology. II: Cohomology of Groups and Modules (1998) [4] DOI: 10.1007/BF01166459 · Zbl 0593.20062 [5] DOI: 10.1007/978-1-4684-9327-6 [6] DOI: 10.1016/0022-4049(81)90081-5 · Zbl 0483.20003 [7] DOI: 10.1007/978-3-0348-9189-9 [8] Carlson J. F., Cohomology of Rings of Finite Groups: With an Appendix: Calculations of Cohomology Rings of Groups of Order Dividing 64 (2003) · Zbl 1056.20039 [9] Chouinard L., J. Pure Appl. Algebra 7 pp 278– [10] Curtis C. W., Representation Theory of Finite Groups and Associative Algebras (1988) · Zbl 0634.20001 [11] Kawai H., Osaka J. Math. 27 pp 937– [12] DOI: 10.1016/S0022-4049(98)90173-6 · Zbl 0955.55009 [13] DOI: 10.1007/BF02566680 · Zbl 0439.20032 [14] O. Talelli, Periodic Cohomology and Free and Proper Actions on Rn {\(\times\)} Sm, London Mathematical Society Lecture Note Series 261 (1997) pp. 701–717. · Zbl 1007.20052 [15] DOI: 10.1112/S0024609305004273 · Zbl 1079.20068 [16] DOI: 10.1007/s00013-006-1160-9 · Zbl 1158.20026 [17] DOI: 10.1016/0022-4049(82)90103-7 · Zbl 0475.20041 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.