Motivated by the study of pro-p groups With finite coclass, we consider the class of pro-p groups with few normal subgroups. This is not a well defined class and we offer several different definitions and study the connections between them. Furthermore, we propose a definition of periodicity for pro-p groups, thus, providing a general framework for some periodic patterns that have already been observed in the existing literature. We then focus oil examples and show that strikingly all the interesting examples not only have few normal Subgroups, but in addition have periodicity in the lattice of normal subgroups. (C) 2008 Elsevier Inc. All rights reserved.
Pro-p groups with few normal subgroups / Y., Barnea; N., Gavioli; A., Jaikin Zapirain; Monti, Valerio; C. M., Scoppola. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 321:2(2009), pp. 429-449. [10.1016/j.jalgebra.2008.10.012]
Pro-p groups with few normal subgroups
MONTI, Valerio;
2009
Abstract
Motivated by the study of pro-p groups With finite coclass, we consider the class of pro-p groups with few normal subgroups. This is not a well defined class and we offer several different definitions and study the connections between them. Furthermore, we propose a definition of periodicity for pro-p groups, thus, providing a general framework for some periodic patterns that have already been observed in the existing literature. We then focus oil examples and show that strikingly all the interesting examples not only have few normal Subgroups, but in addition have periodicity in the lattice of normal subgroups. (C) 2008 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
