On a cohomological characterization of free profinite products of three profinite groups with amalgamated subgroups
DOI:
https://doi.org/10.17398/Keywords:
pro-C group, pro-C topology, free pro-C product of pro-C groups with amalgamation, free pro-C product of pro-C groups with commuting subgroups, group of continuous derivationsAbstract
Let C be the class of all finite solvable groups and n ≥ 2 be an integer. In this paper, we present constructions of free pro-C products of n pro-C groups with amalgamated subgroups, and of free pro-C products of n pro-C groups with commuting subgroups. We also provide conditions under which a given free pro-C product of three pro-C groups with amalgamated subgroups can be written as a free pro-C product with amalgamated subgroup of two free pro-C products with amalgamated subgroups. Furthermore, we characterize –using cohomological conditions– when a pro-C group is the free pro-C product of three of its subgroups with amalgamated subgroups. Finally, we obtain a similar characterization for free pro-C products of two pro-C groups with commuting subgroups.
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