@MISC{GROUP_12.MIZ,
  AUTHOR = {Okazaki, Hiroyuki and Arai, Kenichi and Shidama, Yasunari},
  TITLE = {Normal Subgroup of Product of Groups},
  SECTION1 = {Normal Subgroup of Product of Groups},
  SECTION2 = {Product of Subgroups of a Group},
  DAY = {2},
  MONTH = {July},
  YEAR = {2010},
  ADDRESS1 = {Shinshu University, Nagano, JAPAN},
  ADDRESS2 = {Shinshu University, Nagano, JAPAN},
  ADDRESS3 = {Shinshu University, Nagano, JAPAN},
  SUMMARY = {In \cite{GROUP_7.ABS} it was formalized that
    the direct product of a family of groups gives a new group.
    In this article, we formalize that for all $j$ \in I$,
    the group $G =\Pi_{i \in I} G_i$ has a normal subgroup
    isomorphic to $G_j$. Moreover we show some relations
    between a family of groups and its direct product.}}

