For n a positive integer, a group G is called core-n if H/H_G has order at most n for every subgroup H of G (where H_G is the normal core of H, the largest normal subgroup of G contained in H). It is proved that a finite core-p p-group G has a normal abelian subgroup whose index in G is at mostp 2 if p>2, which is the best possible bound, and at most 2^6 if p=2.
Finite core-p p-groups / Cutolo, Giovanni; E. I., Khukhro; J. C., Lennox; S., Rinauro; H., Smith; J., Wiegold. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 188:2(1997), pp. 701-719. [10.1006/jabr.1996.6811]
Finite core-p p-groups
CUTOLO, GIOVANNI;
1997
Abstract
For n a positive integer, a group G is called core-n if H/H_G has order at most n for every subgroup H of G (where H_G is the normal core of H, the largest normal subgroup of G contained in H). It is proved that a finite core-p p-group G has a normal abelian subgroup whose index in G is at mostp 2 if p>2, which is the best possible bound, and at most 2^6 if p=2.File in questo prodotto:
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