On groups with root system of type .
Oueslati, H. (2009)
Beiträge zur Algebra und Geometrie
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Oueslati, H. (2009)
Beiträge zur Algebra und Geometrie
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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...
Otera, Daniele Ettore, Russo, Francesco G. (2010)
International Journal of Mathematics and Mathematical Sciences
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P. Głowacki (1979)
Colloquium Mathematicae
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Dwyer, W.G. (1998)
Documenta Mathematica
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Adolf Mader, Otto Mutzbauer (2001)
Colloquium Mathematicae
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We study direct decompositions of extensions of rigid completely decomposable groups by finite primary groups. These decompositions are unique and can be found by finite procedures. By passing to certain quotients the determination of the direct decompositions is made more efficient.
Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki, Yasunari Shidama (2016)
Formalized Mathematics
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In this article, conservation rules of the direct sum decomposition of groups are mainly discussed. In the first section, we prepare miscellaneous definitions and theorems for further formalization in Mizar [5]. In the next three sections, we formalized the fact that the property of direct sum decomposition is preserved against the substitutions of the subscript set, flattening of direct sum, and layering of direct sum, respectively. We referred to [14], [13] [6] and [11] in the formalization. ...
Daya-Nand Verma (1971)
Annales scientifiques de l'École Normale Supérieure
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Stein, Alexander (1998)
Beiträge zur Algebra und Geometrie
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Muhammad A. Albar, Walid M. Al-Hamdan (1993)
Rendiconti del Seminario Matematico della Università di Padova
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S. Midura, J. Tabor (1978)
Annales Polonici Mathematici
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Colin C. Graham (1978)
Colloquium Mathematicae
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Moszkowski, Paul (1994)
Séminaire Lotharingien de Combinatoire [electronic only]
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S. V. Jablan (1987)
Matematički Vesnik
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