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We investigate the structure of finite groups G in which gcd(χ(1),∣G:kerχ∣/χ(1))=1 for all irreducible characters χ of G. [ABSTRACT FROM AUTHOR]

A group G is said to satisfy the maximal permutizer condition if the permutizer of any maximal subgroup M of G is equal to G. In this note, a characterization is given of finite groups which satisfy the maximal permutizer condition. [ABSTRACT FROM AUTHOR]

Let G be a finite group. Let μ(G) be the quotient of the order of group G and k(G) the number of conjugacy classes of G. In this paper, we investigate the connection between μ (C) and the structure of finite groups. [ABSTRACT FROM AUTHOR]

Let bcl(G) denote the largest conjugacy class length of a finite group G. In this note, we prove that if bcl(G)

It is shown that if a finite group G possesses precisely four irreducible character de- grees 1, m , n, mn, then G is solvable. Furthermore, one of following statements holds: the derived length of G is at most 3; cd (G) = {1, 3, 13, 39}; or cd (G) = {1, pr1, pr2, p r1+r2} for some prime p. [ABSTRACT FROM AUTHOR]

In this article, a statistical score method for comparison of partial genomic regions in their representatives of full-length genome of hepatitis E virus (HEV) for genotyping was developed. The critical values of the statistics for hypothesis testing were generated through Monte Carlo simulations. It was found that fragment III might be a statistically representative region for the whole genome of HEV for genotyping. Based on both the full-length sequence and fragment III, the same four genotypes were identified by the subsequent phylogenetic analysis, and similar ranges of mean nucleotide difference were also observed to differentiate HEV sequences at the three levels genotype, subtype and isolate, which further verified the statistical results. It may be concluded from this study that the score method is effective for comparing partial genomic regions with full-length genome of HEV strains for genotyping. Copyright © 2007 S. Karger AG, Basel [ABSTRACT FROM AUTHOR]