Maximal subgroups of the semigroup of relations
β Scribed by J.S Montague; R.J Plemmons
- Publisher
- Elsevier Science
- Year
- 1969
- Tongue
- English
- Weight
- 656 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We determine all maximal subgroups of the direct product G n of n copies of a group G. If G is finite, we show that the number of maximal subgroups of G n is a quadratic function of n if G is perfect, but grows exponentially otherwise. We deduce a theorem of Wiegold about the growth behaviour of the
We show that S n has at most n 6Γ11+o(1) conjugacy classes of primitive maximal subgroups. This improves an n c log 3 n bound given by Babai. We conclude that the number of conjugacy classes of maximal subgroups of S n is of the form ( 12 +o(1))n. It also follows that, for large n, S n has less than