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 on 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. © 2008 Elsevier Inc. All rights reserved.

Pro-p groups with few normal subgroups

Monti V.;
2009-01-01

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 on 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. © 2008 Elsevier Inc. All rights reserved.
2009
Just infinite pro-p groups; Normal subgroup growth; Periodicity
Barnea, Y.; Gavioli, N.; Jaikin-Zapirain, A.; Monti, V.; Scoppola, C. M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2105492
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