ItÔ's Theorem on Groups with two class sizes revisited
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadatos
Título
ItÔ's Theorem on Groups with two class sizes revisitedFecha de publicación
2012-06Editor
Australian Mathematical Publishing Association; Cambridge University PressISSN
0004-9727; 1755-1633Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8559738 ...Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
LetG be a finite p-solvable group. We prove that ifG has exactly two conjugacy class sizes of p
0
-elements
of prime power order, say 1 and m, then m = p
aq
b
, for two distinct primes p and q, and G either has ... [+]
LetG be a finite p-solvable group. We prove that ifG has exactly two conjugacy class sizes of p
0
-elements
of prime power order, say 1 and m, then m = p
aq
b
, for two distinct primes p and q, and G either has an
abelian p-complement or G = PQ A, with P and Q a Sylow p-subgroup and a Sylow q-subgroup of
G, respectively, and A is abelian. In particular, we provide a new extension of Itô’s theorem on groups
having exactly two class sizes for elements of prime power order. [-]
Publicado en
Bulletin of the Australian Mathematical Society (2012) Vol. 85, num. 03Derechos de acceso
http://rightsstatements.org/vocab/CNE/1.0/
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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