Two generator subgroups of free products with commuting subgroups
نویسندگان
چکیده
منابع مشابه
on the free profinite products of profinite groups with commuting subgroups
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 comp...
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Proof. Clearly, the image of F is HK by definition. To see that F is injective, suppose that F (h1, k1) = F (h2, k2). Then by definition h1k1 = h2k2. Thus h −1 2 h1 = k2k −1 1 . Since H is a subgroup, h−1 2 h1 ∈ H, and since K is a subgroup, k2k −1 1 ∈ K. Thus h−1 2 h1 = k2k −1 1 ∈ H ∩ K = {1}, and so h −1 2 h1 = k2k −1 1 = 1. It follows that h−1 2 h1 = 1, so that h1 = h2, and similarly k2k −1 ...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2002
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(01)00152-9