Displaying similar documents to “On the composition factors of a group with the same prime graph as B n ( 5 ) ”

Square-free Lucas d -pseudoprimes and Carmichael-Lucas numbers

Walter Carlip, Lawrence Somer (2007)

Czechoslovak Mathematical Journal

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Let d be a fixed positive integer. A Lucas d -pseudoprime is a Lucas pseudoprime N for which there exists a Lucas sequence U ( P , Q ) such that the rank of N in U ( P , Q ) is exactly ( N - ε ( N ) ) / d , where ε is the signature of U ( P , Q ) . We prove here that all but a finite number of Lucas d -pseudoprimes are square free. We also prove that all but a finite number of Lucas d -pseudoprimes are Carmichael-Lucas numbers.

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 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.

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...