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Journal of Applied Mathematics
Volume 2012, Article ID 484805, 11 pages
Research Article

Some Results on Equivalence Groups

School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa

Received 28 August 2012; Accepted 1 October 2012

Academic Editor: Fazal M. Mahomed

Copyright © 2012 J. C. Ndogmo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The comparison of two common types of equivalence groups of differential equations is discussed, and it is shown that one type can be identified with a subgroup of the other type, and a case where the two groups are isomorphic is exhibited. A result on the determination of the finite transformations of the infinitesimal generator of the larger group, which is useful for the determination of the invariant functions of the differential equation, is also given. In addition, the Levidecomposition of the Lie algebra associated with the larger group is found; the Levi factor of which is shown to be equal, up to a constant factor, to the Lie algebra associated with the smaller group.