In amplitude modulation, the modulation index m, is kept less than or equal to 1 because

1
m > 1, will result in interference between carrier frequency and message frequency, resulting into distortion.
2
m < 1 will result in overlapping of both side bands resulting into loss of information.
3
m > 1 will result in change in phase between carrier signal and message signal.
4
m > 1 indicates amplitude of message signal greater than amplitude of carrier signal resulting into distortion.

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