Partitions of Groups into Large Subsets
โ Scribed by I. V. Protasov
- Book ID
- 110433116
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 2003
- Tongue
- English
- Weight
- 99 KB
- Volume
- 73
- Category
- Article
- ISSN
- 0001-4346
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
A subset of a group is said to be product-free if the product of two of its elements is never itself an element of the subset. Using the classification of finite simple groups, we prove that every finite group of order n has a product-free subset of more than cn 11ร14 elements, for some fixed c>0. T
For I G t < k CI u. let S(t, k, u) denote a Steiner system and let Pr, (u) be the set of all k-subsets of theset {i,2,..., u}. We partition PJ 13) into 55 mutually disjoint S(2.4, 13)'s (projective planes). This is the first known example of a complete partition of Pk(u) into disjoint S(t, k, u)'s f
Let r 3 1 be a tied positive integer. We give the limiting distribution for the probability that the vertices of a random graph can be partitioned equitably into I cycles.