@MISC{GROUP_19.MIZ,
  AUTHOR = {Nakasho, Kazuhisa and Yamazaki, Hiroshi and Okazaki, Hiroyuki and Shidama, Yasunari},
  TITLE = {Definition and Properties of Direct Sum Decomposition of Groups},
  SECTION1 = {Miscellanies},
  SECTION2 = {Support of Element of Direct Product Group},
  SECTION3 = {Product Map and Sum Map},
  SECTION4 = {Definition of Internal and External Direct Sum Decomposition},
  SECTION5 = {Equivalent Expression of Internal Direct Sum Decomposition},
  DAY = {31},
  MONTH = {December},
  YEAR = {2014},
  ADDRESS2 = {Shinshu University, Nagano, JAPAN},
  ADDRESS2 = {Shinshu University, Nagano, JAPAN},
  ADDRESS3 = {Shinshu University, Nagano, JAPAN},
  ADDRESS4 = {Shinshu University, Nagano, JAPAN},
  SUMMARY = {In this article, direct sum decomposition of group is mainly
   discussed. In the second section, support of element of direct product group
   is defined and its properties are formalized. It is formalized here the fact
   that an element of direct product group belongs to its direct sum if and only
   if support of the element is finite. In the third section, product map and
   sum map are prepared. In the forth section, internal and external direct sum
   are defined. In the last section, an equivalent form of internal direct sum
   is proved.},
  ACKNOWLEDGEMENT = {This work was supported by JSPS KAKENHI 22300285.}}
