This is an announcement for the paper "A note on the Busemann-Petty problem for bodies of certain invariance" by Marisa Zymonopoulou. Abstract: The Busemann-Petty problem asks whether origin symmetric convex bodies in $\R^n$ with smaller hyperplane sections necessarily have smaller volume. The answer is affirmative if $n\leq 3$ and negative if $n\geq 4.$ We consider a class of convex bodies that have a certain invariance property with respect to their ordered k-tuples of coordinates in $\R^{kn}$ and prove the corresponding problem. Archive classification: math.FA The source file(s), kn.tex: 32692 bytes, is(are) stored in gzipped form as 0811.1593.gz with size 10kb. The corresponding postcript file has gzipped size 82kb. Submitted from: marisa@cwru.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.1593 or http://arXiv.org/abs/0811.1593 or by email in unzipped form by transmitting an empty message with subject line uget 0811.1593 or in gzipped form by using subject line get 0811.1593 to: math@arXiv.org.