12 research outputs found
The average element order and the number of conjugacy classes of finite groups
Let be the average order of the elements of , where is a finite group. We show that there is no polynomial lower bound for in terms of , where , even when is a prime-power order group and is abelian. This gives a negative answer to a question of A. Jaikin-Zapirain
Nilpotent and abelian Hall subgroups in finite groups
First published in Transactions of the American Mathematical Society in volume 368 and number 4, APR 2016, published by the American Mathematical Society[EN] We give a characterization of the finite groups having nilpotent or abelian Hall pi-subgroups that can easily be verified using the character table.The research of the first, second, fourth, fifth, and sixth authors was supported by the Prometeo/Generalitat Valenciana, Proyectos MTM2010-15296, MTM2010-19938-C03-02 Fundacio Bancaixa P11B2010-47 and Fondos Feder. The third author gratefully acknowledges financial support by ERC Advanced Grant 291512. The seventh author was supported by the NSA (grant H98230-13-1-0229). The eighth author gratefully acknowledges the support of the NSF (grants DMS-0901241 and DMS-1201374).Beltran, A.; Felipe Román, MJ.; Malle, G.; Moreto Quintana, A.; Navarro Ortega, G.; Sanus Vitoria, L.; Solomon, R.... (2016). Nilpotent and abelian Hall subgroups in finite groups. Transactions of the American Mathematical Society. 368(4):2497-2513. https://doi.org/10.1090/tran/6381S24972513368
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Criminals : suggestions to improve security procedures
Security procedures are considered a critical component of an organization’s overall security program (Dunham 2018). They provide guidance on how to implement, enable and enforce existing security controls; and on how to execute security relevant business processes in a consistent and concerted manner (Ibid.). At the same time, they are to be considered controls in their own right. Same as other components of a security program, they require constant fine-tuning in order to remain effective and efficient over time. This entry highlights a number of triggers or incentives for organizations to upgrade existing security procedures or to implement new ones. It further positions script analysis as a promising tool to ensure that controls and procedures remain effective and fit for purpose