Influence of minimal subgroups on the product of smooth groups

Abdelmoneim M. Elkholy; M. H. Abd El-Latif

doi:10.14419/ijbas.v4i2.4182

Authors

Abdelmoneim M. Elkholy Mathematics Department, Faculty of Science, Beni Suef University, Beni-Suef 62511, Egypt.
M. H. Abd El-Latif

DOI:

https://doi.org/10.14419/ijbas.v4i2.4182

Published:

2015-03-11

Keywords:

Permutable subgroups, Smooth groups, Subgroup lattices.

Abstract

A maximal chain in a finite lattice L is called smooth if any two intervals of the same length are isomorphic. We say that a finite group G is totally smooth if all maximal chains in its subgroup lattice L(G) are smooth. In this article, we study the product of finite groups which have a permutable subgroup of prime order under the assumption that the maximal subgroups are totally smooth.

References

[1] A. M. Elkholy, "On totally smooth groups", Int. J. Algebra, Vol.1, No.2, (2007), pp.63-70.

[2] K. Doerk, T. Hawkes, Finite soluble groups. Walter de Gruyter, Berlin-New York, (1992).

[3] M. Asaad, Shaalan, "On the supersolvability of finite groups", Arch. Math, 53, (1989), pp.318-326.

[4] R. Schmidt, "Smooth groups", Geometriae Dedicata, 84, (2001), pp.183-206.

[5] R. Schmidt, "Smooth p-groups", J. Algebra, 234, (2000), pp.533-5390.

[6] R. Schmidt, Subgroup lattices of groups. Walter de Gruyter, Berlin-New York, Berlin-New York, (1994).