On finite 2-equilibrated p-groups
-
Jiao Wang
and
Xiuyun Guo
Abstract
A finite group G is said to be n-equilibrated if,
for all subgroups H and K of G with
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11371237
Funding statement: The research of the work was partially supported by the National Natural Science Foundation of China (11371237) and a grant of “The First-Class Discipline of Universities in Shanghai”. The corresponding author is Xiuyun Guo.
The authors would like to thank Professor Christopher W. Parker for valuable suggestions and comments that contributed to the version of this paper.
References
[1] Beidleman J., Hauck P. and Heineken H., Totally permutable products of certain classes of finite groups, J. Algebra 276 (2004), 826–835. 10.1016/j.jalgebra.2003.12.024Search in Google Scholar
[2] Berkovich Y., Groups of Prime Power Order. Vol. I, Walter de Gruyter, Berlin, 2008. 10.1515/9783110208238Search in Google Scholar
[3] Berkovich Y., Research problems and themes IV, in preparation. 10.1515/9783110281477-061Search in Google Scholar
[4] Berkovich Y. and Janko Z., Groups of Prime Power Order. Vol. II, Walter de Gruyter, Berlin, 2011. Search in Google Scholar
[5] Blackburn N., Deaconescu M. and Mann A., Finite equilibrated groups, Math. Proc. Cambridge Philos. Soc. 120 (1996), 579–588. 10.1017/S0305004100001560Search in Google Scholar
[6] Cao J. J. and Guo X. Y., Finite soluble groups in which the normalizer of every non-normal cyclic subgroup is maximal, J. Group Theory 17 (2014), 671–687. 10.1515/jgt-2014-0004Search in Google Scholar
[7] Cossey J. and Stonehewer S. E., Cyclic permutable subgroups of finite groups, J. Aust. Math. Soc. 71 (2001), 169–176. 10.1017/S1446788700002810Search in Google Scholar
[8] de Giovanni F., Musella C. and Sysak Y. P., Groups with almost modular subgroup lattice, J. Algebra 243 (2001), 738–764. 10.1006/jabr.2001.8886Search in Google Scholar
[9] Huppert B., Endliche Gruppen I, Springer, Berlin, 1967. 10.1007/978-3-642-64981-3Search in Google Scholar
[10] Iwasawa K., Über die endlichen Gruppen und die Verbände ihrer Untergruppen, J. Fac. Sci. Imp. Univ. Tokyo. Sect. I 4 (1941), 171–199. Search in Google Scholar
[11]
Laffey T. J.,
The minimum number of generators of a finite
[12]
Li S. R.,
The structure of
[13]
Li X. H. and Zhang J. Q.,
Finite
[14] Newman M., Subgroups of the modular group and sums of squares, Amer. J. Math. 82 (1960), 761–778. 10.2307/2372938Search in Google Scholar
[15] Rédei L., Das schiefe Produkt in der Gruppentheorie, Comment. Math. Helv. 20 (1947), 225–264. 10.1007/BF02568131Search in Google Scholar
[16] Schmid P., Subgroups permutable with all Sylow subgroups, J. Algebra 207 (1998), 285–293. 10.1006/jabr.1998.7429Search in Google Scholar
[17] Schmidt R., Modular subgroups of finite groups. II, Illinois J. Math. 14 (1970), 344–362. 10.1215/ijm/1256053189Search in Google Scholar
[18]
Silberberg G.,
Finite equilibrated
[19]
Xu M. Y., An L. J. and Zhang Q. H.,
Finite
[20] Xu M. Y. and Qu H. P., Finite p-Groups (in Chinese), Peking University Press, Beijing, 2010. Search in Google Scholar
[21]
Xu M. Y. and Zhang Q. H.,
A classification of metacyclic
[22]
Zhang Q. H., Sun C. J., Qu H. P. and Xu M. Y.,
Finite
[23]
Zhang X. H. and Guo X. Y.,
Finite
[24] Zimmermann I., Submodular subgroups in finite groups, Math. Z. 202 (1989), 545–557. 10.1007/BF01221589Search in Google Scholar
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Codegrees and nilpotence class of p-groups
- On finite 2-equilibrated p-groups
- Minimal dimension of faithful representations for p-groups
- On the Christensen–Wang bounds for the ghost number of a p-group algebra
-
A family of non-Schurian p-Schur rings over groups of order
- Endo-trivial modules for finite groups with dihedral Sylow 2-subgroup
- Symmetric powers of Nat SL(2,𝕂)
- Nested GVZ-groups
- On some groups generated by involutions
-
Thompson’s conjecture for finite simple groups of Lie type
Articles in the same Issue
- Frontmatter
- Codegrees and nilpotence class of p-groups
- On finite 2-equilibrated p-groups
- Minimal dimension of faithful representations for p-groups
- On the Christensen–Wang bounds for the ghost number of a p-group algebra
-
A family of non-Schurian p-Schur rings over groups of order
- Endo-trivial modules for finite groups with dihedral Sylow 2-subgroup
- Symmetric powers of Nat SL(2,𝕂)
- Nested GVZ-groups
- On some groups generated by involutions
-
Thompson’s conjecture for finite simple groups of Lie type
