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In this paper, we investigate equigeodesics on a compact homogeneous space$M=G/H.$ We introduce a formula for the identification of equigeodesic vectorsonly relying on the isotropy representation of $M$ and the Lie structure of theLie algebra of $G$. Applications to $M$-spaces are also discussed.

Equigeodesic vectors on compact homogeneous spaces with equivalent isotropy summands