منابع مشابه
Some Examples of Wallpaper Groups
In this note we discuss some symmetry groups as nice examples of group extensions. We begin by a short general discussion of symmetry groups. An isometry of R is a distancepreserving bijection of R. For examples of isometries, translations by a vector, rotations about a point, and reflections about a hyperplane are all isometries. Let Isom(R) be the set of all isometries of R. This is a group u...
متن کاملSome Examples and Remarks Concerning Groups
We present some examples and remarks which may be helpful to those who are dealing with an abstract algebra or a first semester group theory course. Alternating groups, dihedral groups, and symmetric groups of small orders are treasure troves of elementary examples and counter examples concerning groups. Mathematics Subject Classification: 20-01, 20-02, 20B05, 20B07, 20E06
متن کاملSome Nonprojective Subgroups of Free Topological Groups
For the free topological group on an interval [a, b] a family of closed, locally path-connected subgroups is given such that each group is not projective and so not free topological. Simplicial methods are used, and the test for nonprojectivity is nonfreeness of the group of path components. Similar results are given for the abelian case. Introduction. Let F(X) be the free topological group on ...
متن کاملSome Results Related to Topological Groups via Ideal Topological Spaces
An ideal on a set X is a nonempty collection of subsets of X with heredity property which is also closed finite unions. The concept of Γδ : P(X)→ τ defined as follows for every A ∈ X, Γδ(A) = {x ∈ X : there exists a U ∈ τ δ(x) such that U − A ∈ I}, was introduced by Al-Omari and Hatir [1]. In this paper, we introduce and study δ∗-homeomorphism and Γδ-homeomorphism. Also we give some application...
متن کاملExamples of non-quasicommutative semigroups decomposed into unions of groups
Decomposability of an algebraic structure into the union of its sub-structures goes back to G. Scorza's Theorem of 1926 for groups. An analogue of this theorem for rings has been recently studied by A. Lucchini in 2012. On the study of this problem for non-group semigroups, the first attempt is due to Clifford's work of 1961 for the regular semigroups. Since then, N.P. Mukherjee in 1972 studied...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1966
ISSN: 0025-5645
DOI: 10.2969/jmsj/01820147