caa a22 4500 606200703 CHVBK 20210128100945.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s00025-014-0397-z doi (NATIONALLICENCE)springer-10.1007/s00025-014-0397-z Harris Morton Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, 851 South Morgan Street, 60607-7045, Chicago, IL, USA aut Central Products of Subgroups and Block Theory of Finite Groups [Elektronische Daten] [Morton Harris] Let $${\mathfrak{A}}$$ A be a set of subgroups of the finite group G that form a central product M and such that G permutes the subgroups in $${\mathfrak{A}}$$ A by conjugation so that $${M\trianglelefteq G}$$ M ⊴ G . (For example, $${\mathfrak{A}}$$ A could be the set of components of G). We show that the conjugation action of G on M can be "lifted” to an action of G on the direct product of the subgroups in $${\mathfrak{A}}$$ A . Then we apply this procedure to obtain a Clifford theoretic reduction for an arbitrary p-block of G. Also we show that, in some cases, additional reductions can be applied. Springer Basel, 2014 Results in Mathematics Springer Basel 67/1-2(2015-02-01), 111-124 1422-6383 67:1-2<111 2015 67 25 https://doi.org/10.1007/s00025-014-0397-z 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/s00025-014-0397-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Harris Morton Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, 851 South Morgan Street, 60607-7045, Chicago, IL, USA aut NATIONALLICENCE 773 0- Results in Mathematics Springer Basel 67/1-2(2015-02-01), 111-124 1422-6383 67:1-2<111 2015 67 25