A group G is core-2 if and only if |H/H_G| is at most 2 for every subgroup H of G. We prove that every core-2 nilpotent 2-group of class 2 has an abelian subgroup of index at most 4. This bound is the best possible. As a consequence, every 2-group satisfying the property core-2 has an abelian subgroup of index at most 16.
On core-2 groups / Cutolo, Giovanni; H., Smith; J., Wiegold. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 237:2(2001), pp. 813-841. [10.1006/jabr.2000.8599]
On core-2 groups
CUTOLO, GIOVANNI;
2001
Abstract
A group G is core-2 if and only if |H/H_G| is at most 2 for every subgroup H of G. We prove that every core-2 nilpotent 2-group of class 2 has an abelian subgroup of index at most 4. This bound is the best possible. As a consequence, every 2-group satisfying the property core-2 has an abelian subgroup of index at most 16.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
