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• # Artykuł - szczegóły

## Formalized Mathematics

2011 | 19 | 1 | 23-26

## Normal Subgroup of Product of Groups

EN

### Abstrakty

EN
In [6] 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 ∈ I, the group G = Πi∈IGi has a normal subgroup isomorphic to Gj. Moreover, we show some relations between a family of groups and its direct product.

23-26

wydano
2011-01-01
online
2011-07-18

### Twórcy

autor
• Shinshu University, Nagano, Japan
autor
• Shinshu University, Nagano, Japan
autor
• Shinshu University, Nagano, Japan

### Bibliografia

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• [5] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
• [6] Artur Korniłowicz. The product of the families of the groups. Formalized Mathematics, 7(1):127-134, 1998.
• [7] Wojciech A. Trybulec. Classes of conjugation. Normal subgroups. Formalized Mathematics, 1(5):955-962, 1990.
• [8] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
• [9] Wojciech A. Trybulec. Subgroup and cosets of subgroups. Formalized Mathematics, 1(5):855-864, 1990.
• [10] Wojciech A. Trybulec. Lattice of subgroups of a group. Frattini subgroup. Formalized Mathematics, 2(1):41-47, 1991.
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