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Why is the kernel cyclic if and only if the walk does not backtrack?

I'm reading Mathematics of Isogeny Based Cryptography by Luca De Feo. At some point (pg. 32), he says "A walk of length $e_A$ in the $l_A$-isogeny graph corresponds to a kernel of size $l_A^{e_A};...
Manuel Bravi's user avatar