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Reference.org
Universal embedding theorem
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<p>The universal embedding theorem, or Krasner–Kaloujnine universal embedding theorem, is a theorem from the mathematical discipline of <a href="/facts/Group_theory/NfowcI5H">group theory</a> first published in 1951 by <a href="/facts/Marc_Krasner/5mfN68zh">Marc Krasner</a> and <a href="/facts/Lev_Kaluznin/bnEKY3Ma">Lev Kaluznin</a>. The theorem states that any <a href="/facts/Group_extension/pGoe0l4d">group extension</a> of a group <i>H</i> by a group <i>A</i> is isomorphic to a subgroup of the regular <a href="/facts/Wreath_product/zNNX9Q9G">wreath product</a> <i>A</i> Wr <i>H</i>. The theorem is named for the fact that the group <i>A</i> Wr <i>H</i> is said to be <i><a href="/facts/Universal_property/5XJBYMNz">universal</a></i> with respect to all extensions of <i>H</i> by <i>A</i>. </p>