Abstract
Let G be a group. In this note we define conjugate closed groups, which are briefly called CC — Groups. These groups form a proper subclass of T — Groups. We prove that if G = Z(G) × H, then G is conjugate closed if and only if H is conjugate closed. We also show that a finite group G is semisimple, conjugate closed and perfect if and only if it is a direct product of non-abelian and simple groups.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W. Fiet and J. G. Thompson, Solvability of groups of odd order, Pacific. J. Math., 13 (1963), 775–1029.
L. C. Kappe and J. Kirtland, Finite groups with trivial Frattini subgroup, Archiv der mathematik, 80 (2003), 225–234.
S. Mclane, Homology, Springer-Verlag, New York, 1963.
D. J. S. Robinson, Groups in which normality is a transitive relation, Proc. Cambridge Philos. Soc., 60 (1964), 21–38.
D. J. S. Robinson, A Course in the Theory of Groups. (2nd edition), Springer-Verlag, New York.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Karan, R., Narain, S. Some remarks on conjugate closed groups. Indian J Pure Appl Math 42, 249–257 (2011). https://doi.org/10.1007/s13226-011-0017-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13226-011-0017-5