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Reference.org
Kurosh subgroup theorem
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<p>In the <a href="/facts/Mathematics/pxTouaz4">mathematical</a> field of <a href="/facts/Group_theory/NfowcI5H">group theory</a>, the Kurosh subgroup theorem describes the algebraic structure of <a href="/facts/Subgroup/r91mBgpa">subgroups</a> of <a href="/facts/Free_product/bJsMaMGD">free products</a> of <a href="/facts/Group_(mathematics)/IQTYqINt">groups</a>. The theorem was obtained by <a href="/facts/Aleksandr_Gennadievich_Kurosh/ACYN3SPS">Alexander Kurosh</a>, a Russian mathematician, in 1934. Informally, the theorem says that every subgroup of a free product is itself a free product of a <a href="/facts/Free_group/zPo2NIGb">free group</a> and of its intersections with the <a href="/facts/Conjugate_(group_theory)/AFuPIFNW">conjugates</a> of the factors of the original free product. </p>