Proof of a conjecture on the Sperner property of the subgroup lattice of an abelianp-group
β Scribed by Jun Wang
- Publisher
- Springer
- Year
- 1998
- Tongue
- English
- Weight
- 927 KB
- Volume
- 2
- Category
- Article
- ISSN
- 0218-0006
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We will show that for any integer n G 0, the automorphism group of an abelian p-group G, p G 3, contains a unique subgroup which is maximal with respect to being normal and having exponent less than or equal to p n . This subgroup is βΈ l Fix p n G, where βΈ is the unique maximal normal p-subgroup of
In this paper, a formula is given for the Mo bius number +(1, S n ) of the subgroup lattice of the symmetric group S n . This formula involves the Mo bius numbers of certain transitive subgroups of S n . When n has at most two (not necessarily distinct) prime factors or n is a power of two, this for