The structure of the factor group of the unrestricted sum by the restricted sum of Abelian groups II
K. Golema, Andrzej Hulanicki (1964)
Fundamenta Mathematicae
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K. Golema, Andrzej Hulanicki (1964)
Fundamenta Mathematicae
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Peter Vassilev Danchev, Patrick Keef (2008)
Archivum Mathematicum
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We prove that pure subgroups of thick Abelian -groups which are modulo countable are again thick. This generalizes a result due to Megibben (Michigan Math. J. 1966). Some related results are also established.
Kazuhisa Nakasho, Hiroyuki Okazaki, Hiroshi Yamazaki, Yasunari Shidama (2015)
Formalized Mathematics
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In this article, the equivalent expressions of the direct sum decomposition of groups are mainly discussed. In the first section, we formalize the fact that the internal direct sum decomposition can be defined as normal subgroups and some of their properties. In the second section, we formalize an equivalent form of internal direct sum of commutative groups. In the last section, we formalize that the external direct sum leads an internal direct sum. We referred to [19], [18] [8] and...
Danchev, Peter (2010)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki, Yasunari Shidama (2015)
Formalized Mathematics
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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 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 fourth section, internal and external direct sum are defined. In the last section, an equivalent form...
Kuzennyi, N.F., Subbotin, I.Ya. (2005)
International Journal of Mathematics and Mathematical Sciences
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Gilbert Baumslag (1974)
Compositio Mathematica
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Firat Ates, A. Sinan Çevik (2009)
Rendiconti del Seminario Matematico della Università di Padova
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