There have been hundreds of suspects but none seem to be the definitive killer. She was given the name "Black Dahlia" - her brutal death has been sensationalized by reporters of the media. This is among one of history's coldest, most gory and most brutal cases. This is the case of the Black Dahlia.
Sources:
https://www.fbi.gov/history/famous-cases/black-dahlia
https://allthatsinteresting.com/black-dahlia-elizabeth-short
https://en.wikipedia.org/wiki/Black_Dahlia
https://en.wikipedia.org/wiki/Hemicorporectomy
If you’d like to see documented photos of Elizabeth’s body:
(Warning: graphic description and images)
https://www.reelreviews.com/shorttakes-56/morbidly-hollywood-no-ad/black-dahlia-death3
