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2013 | 21 | 1 | 65-74
Tytuł artykułu

Isomorphisms of Direct Products of Finite Commutative Groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We have been working on the formalization of groups. In [1], we encoded some theorems concerning the product of cyclic groups. In this article, we present the generalized formalization of [1]. First, we show that every finite commutative group which order is composite number is isomorphic to a direct product of finite commutative groups which orders are relatively prime. Next, we describe finite direct products of finite commutative groups
Słowa kluczowe
Wydawca
Rocznik
Tom
21
Numer
1
Strony
65-74
Opis fizyczny
Daty
wydano
2013-01-01
Twórcy
  • Shinshu University Nagano, Japan
  • Shinshu University Nagano, Japan
  • Shinshu University Nagano, Japan
Bibliografia
  • [1] Kenichi Arai, Hiroyuki Okazaki, and Yasunari Shidama. Isomorphisms of direct products of finite cyclic groups. Formalized Mathematics, 20(4):343-347, 2012. doi:10.2478/v10037-012-0038-5.[Crossref]
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  • [6] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
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  • [11] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [12] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [13] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
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  • [16] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.
  • [17] Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relatively primes. Formalized Mathematics, 1(5):829-832, 1990.
  • [18] Beata Madras. Product of family of universal algebras. Formalized Mathematics, 4(1): 103-108, 1993.
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  • [22] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
  • [23] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
  • [24] Wojciech A. Trybulec. Subgroup and cosets of subgroups. Formalized Mathematics, 1(5): 855-864, 1990.
  • [25] Wojciech A. Trybulec. Classes of conjugation. Normal subgroups. Formalized Mathematics, 1(5):955-962, 1990.
  • [26] Wojciech A. Trybulec. Lattice of subgroups of a group. Frattini subgroup. FormalizedMathematics, 2(1):41-47, 1991.
  • [27] Wojciech A. Trybulec and Michał J. Trybulec. Homomorphisms and isomorphisms of groups. Quotient group. Formalized Mathematics, 2(4):573-578, 1991.
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  • [29] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_forma-2013-0007
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