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Displaying similar documents to “Active sums I.”

Finite groups with globally permutable lattice of subgroups

C. Bagiński, A. Sakowicz (1999)

Colloquium Mathematicae

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The notions of permutable and globally permutable lattices were first introduced and studied by J. Krempa and B. Terlikowska-Osłowska [4]. These are lattices preserving many interesting properties of modular lattices. In this paper all finite groups with globally permutable lattices of subgroups are described. It is shown that such finite p-groups are exactly the p-groups with modular lattices of subgroups, and that the non-nilpotent groups form an essentially larger class though they...

Normal Subgroup of Product of Groups

Hiroyuki Okazaki, Kenichi Arai, Yasunari Shidama (2011)

Formalized Mathematics

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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.

Isomorphisms of Direct Products of Cyclic Groups of Prime Power Order

Hiroshi Yamazaki, Hiroyuki Okazaki, Kazuhisa Nakasho, Yasunari Shidama (2013)

Formalized Mathematics

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In this paper we formalized some theorems concerning the cyclic groups of prime power order. We formalize that every commutative cyclic group of prime power order is isomorphic to a direct product of family of cyclic groups [1], [18].