Abstract
A group G is defined to be hypocritical if, whenever G is in a locally finite variety V of groups and G is a section closed class of groups which generates V, then G ∈ G. The critical groups which for some prime p are an extension of an abelian p-group by a p′-group are considered from the standpoint of hypocriticality.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Warren Brisley and L.G. Kovács, “On soluble groups of prime power exponent”, Bull. Austral. Math. Soc. 4 (1971), 389–396. MR43#4913.
R,M. Bryant and L.G. Kovâcs, “The skeleton of a variety of groups”, Bull. Austral. Math. Soc. 6 (1972), 357–378. Zb1. 237. 20028.
P.J. Cossey, “On varieties of A-groups”, (PhD thesis, Australian National University, Canberra, 1966 ).
John Cossey, “Critical groups and the lattice of varieties”, Proc. Amer. Math. Soc. 20 (1969), 217–221. HR38#1147.
L.F. Harris, “Varieties and section closed classes of groups”, (PhD thesis, Australian National University, Canberra, 1973; see also, Abstract, Bull. Austral. Math. Soc. 9 (1973), 475–476 ).
L.F. Harris, “A product variety of groups with distributive lattice”, Proc. Amer. Math. Soc. (to appear).
L.G. Kovács and M.F. Newman, “On critical groups”, J. Austral.. Math. Soc. 6 (1966), 237–250. MR34#233.
Hanna. Neumann, Varieties of groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 37. Springer-Verlag, Berlin, Heidelberg, New York, 1967). MR35#6734.
M,F. Newman, “On a class of metabelian groups”, Proc. London Math. Soc. (3) 10 (1960), 354–364. M822#8074.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1974 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Harris, L.F. (1974). Hypocritical and Sincere Groups. In: Newman, M.F. (eds) Proceedings of the Second International Conference on the Theory of Groups. Lecture Notes in Mathematics, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21571-5_30
Download citation
DOI: https://doi.org/10.1007/978-3-662-21571-5_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06845-7
Online ISBN: 978-3-662-21571-5
eBook Packages: Springer Book Archive