International Journal of Mathematics Trends and Technology
Volume 44 | Number 3 | Year 2017 | Article Id. IJMTT-V44P523 | DOI : https://doi.org/10.14445/22315373/IJMTT-V44P523
—In 1970, Menegazzo gave a complete description of the structure of soluble IM-groups, i.e., groups in which every subgroup can be obtained as intersection of maximal subgroups. The work is devoted to the structure of finite nilpotent algebras. Relations between nilpotency and Frattini subgroups are given in this paper.
[1] G. Kaplan, On T-groups, supersolvable groups, and maximal subgroups, Arch.Math. (Basel) 96 (2011), no. 1, 19-25.
[2] G. Frattini, Intornoallagenerazionedeigruppi di operazioni, Rend. Accad. Lincei 4 (1), 281–285 and 455–456.
[3] F. Menegazzo, Gruppineiqualiognisottogruppo èintersezione di sottogruppimassimali, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 48 (1970), 559-562.
[4] B. H. Neumann, Groups with finite classes of conjugate subgroups, Math. Z. 63 (1955) 76-96.
[5] R. Schmidt, Subgroup Lattices of Groups, Walter de Gruyter& Co., Berlin,1994.
[6] H.C. Bhatia, A generalized Frattini subgroup of a finite group. Ph.D. thesis, Michigan State University, East Lansing, 1972.
[7] P. Bhattacharya and N.P. Mukherjee, A generalized Frattini subgroup of finite group, International Journal of Math and Mathematical Science Vol.12 No. 2 (1989) 263-266.
[8] V. I. Zenkov, V. S. Monakhov, D. O. Revin, An Analog for the FrattiniFactorizationof Finite Groups, Algebra and Logic, 43:2 (2004), 102–108.
Mohit James, Ajit Paul, "Nilpotency in Frattini Subgroups," International Journal of Mathematics Trends and Technology (IJMTT), vol. 44, no. 3, pp. 121-122, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V44P523
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