Australia's Hazlewood out of 2nd India Test
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The right-armer, who took five wickets in Australia's 295-run first Test defeat at Perth, has what Cricket Australia described as "a low-grade left side injury".
"Hazlewood will remain with the group in Adelaide to prepare for the remainder of the series," CA added.
While the uncapped Abbott and Doggett were drafted in, Hazelwood's absence is likely to open the door for Scott Boland to play in the day-night Test that starts on Friday.
Boland, who was already part of the squad, played the last of his 10 Tests in July 2023 against England at Headingley.
There are also question marks around allrounder Mitchell Marsh, who, like Hazlewood, pulled up sore following their Perth thrashing.
Beau Webster was on Thursday called into the squad as cover for him.