Alperin's theorem on non-existence of abelian subgroups of large prime power order for prime equal to two
From Groupprops
History
This result was proved in a paper by Alperin in 1965.
Statement
There exists a group of order that does not contain any abelian subgroup of order .
Related facts
- Alperin's theorem on non-existence of abelian subgroups of large prime power order for odd prime
- Existence of abelian normal subgroups of small prime power order
- Abelian-to-normal replacement theorem for prime-cube order
- Abelian-to-normal replacement theorem for prime-fourth order
- Jonah-Konvisser congruence condition on number of abelian subgroups of small prime power order for odd prime
References
Journal references
- Large abelian subgroups of p-groups by Jonathan Lazare Alperin, Transactions of the American Mathematical Society, Volume 117, Page 10 - 20(Year 1965): ^{Official copy}^{More info}