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Equivalent Expressions of Direct Sum Decomposition of Groups1

Kazuhisa Nakasho, Hiroyuki Okazaki, Hiroshi Yamazaki, Yasunari Shidama (2015)

Formalized Mathematics

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 [14] in the...

Factoring an odd abelian group by lacunary cyclic subsets

Sándor Szabó (2010)

Discussiones Mathematicae - General Algebra and Applications

It is a known result that if a finite abelian group of odd order is a direct product of lacunary cyclic subsets, then at least one of the factors must be a subgroup. The paper gives an elementary proof that does not rely on characters.

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