6533b870fe1ef96bd12cfaba
RESEARCH PRODUCT
Large subgroups of a finite group of even order
Bernhard AmbergLev Kazarinsubject
Discrete mathematicsPure mathematicsFinite groupConjugacy classLocally finite groupApplied MathematicsGeneral MathematicsCharacteristic subgroupCentralizer and normalizerMathematicsdescription
It is shown that if G G is a group of even order with trivial center such that | G | > 2 | C G ( t ) | 3 |G|>2|C_{G}(t)|^{3} for some involution t ∈ G t\in G , then there exists a proper subgroup H H of G G such that | G | > | H | 2 |G|> |H|^{2} . If | G | > | C G ( t ) | 3 |G|>|C_{G}(t)|^{3} and k ( G ) k(G) is the class number of G G , then | G | ≤ k ( G ) 3 |G|\leq k(G)^{3} .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-05-10 | Proceedings of the American Mathematical Society |