منابع مشابه
Transversals in non-discrete groups
The concept of ‘topological right transversal’ is introduced to study right transversals in topological groups. Given any right quasigroup S with a Tychonoff topology T , it is proved that there exists a Hausdorff topological group in which S can be embedded algebraically and topologically as a right transversal of a subgroup (not necessarily closed). It is also proved that if a topological rig...
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We prove that a finite group with nilpotent subgroup H and H-connected transversals is solvable. The proof depends on the classification of finite simple groups.
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The intractability of the traditional discrete logarithm problem (DLP) forms the basis for the design of numerous cryptographic primitives. In [2] M. Sramka et al. generalize the DLP to arbitrary finite groups. One of the reasons mentioned for this generalization is P. Shor’s quantum algorithm [4] which solves efficiently the traditional DLP. The DLP for a nonabelian group is based on a particu...
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In group theory nilpotency of a group has a great importance. In this paper we have studied some concept of nilpotency through right transversals. We have also studied prime power groups and frattini subgroups through right transversals.
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It is shown that every set of n integers contains a subset of size Ω(n) in which no element is the average of two or more others. This improves a result of Abbott. It is also proved that for every > 0 and every m > m( ) the following holds. If A1, . . . , Am are m subsets of cardinality at least m each, then there are a1 ∈ A1, . . . , am ∈ Am so that the sum of every nonempty subset of the set ...
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ژورنال
عنوان ژورنال: Proceedings Mathematical Sciences
سال: 2005
ISSN: 0253-4142,0973-7685
DOI: 10.1007/bf02829804