On the 𝑝-length and 𝔘-class of a 𝑝-solvable finite group

References

[1] R. Baer, Der Kern, eine charakteristische Untergruppe, Compos. Math. 1 (1935), 254–283. Search in Google Scholar

[2] S. Bauman, 𝑝-normality and 𝑝-length of a finite group, Math. Z. 87 (1965), 345–347. 10.1007/BF01113204Search in Google Scholar

[3] H. G. Bray, W. E. Deskins, D. Johnson, J. F. Humphreys, B. M. Puttaswamaiah, P. Venzke and G. L. Walls, Between Nilpotent and Solvable, Polygonal, Washington, 1982. Search in Google Scholar

[4] R. A. Bryce and J. Cossey, The Wielandt subgroup of a finite soluble group, J. Lond. Math. Soc. (2) 40 (1989), no. 2, 244–256. 10.1112/jlms/s2-40.2.244Search in Google Scholar

[5] A. R. Camina, The Wielandt length of finite groups, J. Algebra 15 (1970), 142–148. 10.1016/0021-8693(70)90091-8Search in Google Scholar

[6] K. Doerk and T. Hawkes, Finite Solvable Groups, Walter de Gruyter, Berlin, 1992. 10.1515/9783110870138Search in Google Scholar

[7] D. Gorenstein, Finite Groups, Chelsea, New York, 1980. Search in Google Scholar

[8] W. Guo, Structure Theory for Canonical Classes of Finite Groups, Springer, Heidelberg, 2015. 10.1007/978-3-662-45747-4Search in Google Scholar

[9] P. Hall and G. Higman, On the 𝑝-length of 𝑝-soluble groups and reduction theorems for Burnside’s problem, Proc. Lond. Math. Soc. (3) 6 (1956), 1–42. 10.1112/plms/s3-6.1.1Search in Google Scholar

[10] B. Huppert, Endliche Gruppen. I, Grundlehren Math. Wiss. 134, Springer, Berlin, 1967. 10.1007/978-3-642-64981-3Search in Google Scholar

[11] I. M. Isaacs, Finite Group Theory, Grad. Stud. Math. 92, American Mathematical Society, Providence, 2008. Search in Google Scholar

[12] E. A. Ormerod, On the Wielandt length of metabelian 𝑝-groups, Arch. Math. (Basel) 57 (1991), no. 3, 212–215. 10.1007/BF01196849Search in Google Scholar

[13] E. Schenkman, On the norm of a group, Illinois J. Math. 4 (1960), 150–152. 10.1215/ijm/1255455741Search in Google Scholar

[14] R. Schmidt, Subgroup Lattices of Groups, De Gruyter Exp. Math. 14, Walter de Gruyter, Berlin, 1994. 10.1515/9783110868647Search in Google Scholar

[15] N. Su and Y. Wang, On the 𝑝-length and the Wielandt length of a finite 𝑝-soluble group, Bull. Aust. Math. Soc. 88 (2013), no. 3, 453–459. 10.1017/S0004972713000026Search in Google Scholar

[16] H. Wielandt, Über den Normalisator der subnormalen Untergruppen, Math. Z. 69 (1958), 463–465. 10.1007/BF01187422Search in Google Scholar