Nilpotency of p-complements and p-regular conjugacy class sizes
نویسندگان
چکیده
منابع مشابه
p-divisibility of conjugacy class sizes and normal p-complements
LetN be a normal subgroup of a groupG and let p be a prime. We prove that if the p-part of jx j is a constant for every prime-power order element x 2 N n Z.N /, then N is solvable and has normal p-complement.
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We investigate the properties of Lie algebras of characteristic p which satisfy the Engel identity xy" = 0 for some n < p. We establish a criterion which (when satisfied) implies that if a and b are elements of an Engel-n Lie algebra L then abn~2 generates a nilpotent ideal of I. We show that this criterion is satisfied for n = 6, p = 1, and we deduce that if G is a finite m-generator group of ...
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The origin of pairing based cryptosystems is in the MOV attack [10] on the elliptic curve discrete logarithm problem. The attack was first envisioned by Gerhard Frey. The idea was to use the bilinear properties of the Weil pairing to reduce a discrete logarithm problem in an elliptic curve over a finite field Fq to a discrete logarithm problem in Fqk . It is known [1] that most of the time for ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2006.10.007