Child masturbation??

Is it normal for a child to masturbate at a young age? Like 4-6. My mother keeps trying to tell me that she thinks I was sexually abused when I was young because I masturbated at such a young age. I guess she says I would even do it in public. Please keep in mind that my mother is known to lie and over exaggerate. But I was just wondering if it is normal or if I really was as "gross" and "disturbed" as she says I was. She use to make me feel absolutely disgusting about myself because I would maturate.