Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A Kurosh subgroup theorem for free pro- $ \mathcal{C}$-products of pro- $ \mathcal{C}$-groups


Authors: Dion Gildenhuys and Luis Ribes
Journal: Trans. Amer. Math. Soc. 186 (1973), 309-329
MSC: Primary 20F20
MathSciNet review: 0340433
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \mathcal{C}$ be a class of finite groups, closed under finite products, subgroups and homomorphic images. In this paper we define and study free pro- $ \mathcal{C}$-products of pro- $ \mathcal{C}$-groups indexed by a pointed topological space. Our main result is a structure theorem for open subgroups of such free products along the lines of the Kurosh subgroup theorem for abstract groups. As a consequence we obtain that open subgroups of free pro- $ \mathcal{C}$-groups on a pointed topological space, are free pro- $ \mathcal{C}$-groups on (compact, totally disconnected) pointed topological spaces.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20F20

Retrieve articles in all journals with MSC: 20F20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0340433-3
PII: S 0002-9947(1973)0340433-3
Keywords: Profinite group, pro- $ \mathcal{C}$-group, free product, coproduct, projective limit, pointed topological space, compact, totally disconnected
Article copyright: © Copyright 1973 American Mathematical Society