On the free profinite products of profinite groups with commuting subgroups

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In this paper we introduce the construction of free profinite products of profinite groups withcommuting subgroups. We study a particular case: the proper free profinite products of profinite groups with commuting subgroups. We prove some conditions for a free profinite product of profinite groups with commuting subgroups to be proper. We derive some consequences. We also compute profinite completions of free products of (abstract) groups with commuting subgroups.

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