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Tripleableness of pro-c-groups

Published online by Cambridge University Press:  09 April 2009

Lim Chong-Keang
Lim Chong-Keang
Affiliation:
Department of Mathematics, University of Malaya, Kuala Lumpur, Malaysia
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Let C be a nontrivial full subcategory of the category F of finite discrete groups and continuous homomorphisms, closed under subobjects, quotient and finite products. We consider the category PC of pro-C-groups and continuous homomorphisms (i.e. inverse limits of C-groups) which forms a variety in category PF of profinite groups and continuous homomorphisms. The study of pro-Cgroups is motivated by their occurrence as Galois groups of filed extensions in algebraic number thory (see Serre (1965)). The purpose of this paper is to study the tripleableness of the forgetful functors from PC to various underlying categories. It is also shown that PC is equivalent to the category of algebras of the theory of the forgetful functor from C to S (the category of sets and mappings).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 3 , May 1976 , pp. 299 - 309
Copyright
Copyright © Australian Mathematical Society 1976

References

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