Displaying similar documents to “Square-free Lucas d -pseudoprimes and Carmichael-Lucas numbers”

On the composition factors of a group with the same prime graph as B n ( 5 )

Azam Babai, Behrooz Khosravi (2012)

Czechoslovak Mathematical Journal

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Let G be a finite group. The prime graph of G is a graph whose vertex set is the set of prime divisors of | G | and two distinct primes p and q are joined by an edge, whenever G contains an element of order p q . The prime graph of G is denoted by Γ ( G ) . It is proved that some finite groups are uniquely determined by their prime graph. In this paper, we show that if G is a finite group such that Γ ( G ) = Γ ( B n ( 5 ) ) , where n ≥ 6 , then G has a unique nonabelian composition factor isomorphic to B n ( 5 ) or C n ( 5 ) .

Uniformly convex functions II

Wancang Ma, David Minda (1993)

Annales Polonici Mathematici

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Recently, A. W. Goodman introduced the class UCV of normalized uniformly convex functions. We present some sharp coefficient bounds for functions f(z) = z + a₂z² + a₃z³ + ... ∈ UCV and their inverses f - 1 ( w ) = w + d ₂ w ² + d ₃ w ³ + . . . . The series expansion for f - 1 ( w ) converges when | w | < ϱ f , where 0 < ϱ f depends on f. The sharp bounds on | a n | and all extremal functions were known for n = 2 and 3; the extremal functions consist of a certain function k ∈ UCV and its rotations. We obtain the sharp bounds on | a n | and all extremal functions for...

On potentially H -graphic sequences

Meng Xiao Yin, Jian Hua Yin (2007)

Czechoslovak Mathematical Journal

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For given a graph H , a graphic sequence π = ( d 1 , d 2 , ... , d n ) is said to be potentially H -graphic if there is a realization of π containing H as a subgraph. In this paper, we characterize the potentially ( K 5 - e ) -positive graphic sequences and give two simple necessary and sufficient conditions for a positive graphic sequence π to be potentially K 5 -graphic, where K r is a complete graph on r vertices and K r - e is a graph obtained from K r by deleting one edge. Moreover, we also give a simple necessary and sufficient condition...

A remark on supra-additive and supra-multiplicative operators on C ( X )

Zafer Ercan (2007)

Mathematica Bohemica

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M. Radulescu proved the following result: Let X be a compact Hausdorff topological space and π C ( X ) → C ( X ) a supra-additive and supra-multiplicative operator. Then π is linear and multiplicative. We generalize this result to arbitrary topological spaces.

On potentially K 5 - H -graphic sequences

Lili Hu, Chunhui Lai, Ping Wang (2009)

Czechoslovak Mathematical Journal

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Let K m - H be the graph obtained from K m by removing the edges set E ( H ) of H where H is a subgraph of K m . In this paper, we characterize the potentially K 5 - P 4 and K 5 - Y 4 -graphic sequences where Y 4 is a tree on 5 vertices and 3 leaves.