Essex won their second County Championship in three years.
Abbott's match return of 17-86 is the best ever since Laker took 19-90 against Australia in 1956.
The Tamil Nadu batsman has been India's fourth most successful opener in Test cricket with 3880 runs against his name at an average of 39.19
With a six-wicket win, Middlesex also registered a place in the quarterfinals of the Vitality T20 Blast.
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With 12 points, Surrey have a slim chance of progressing to the quarter-finals.
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The 35-year-old opener replaces Azhar Ali, who has returned to play in Pakistan.
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Last season, Vijay had scores of 56, 100, 85, 80 and 2 for Essex an averaged a healthy 64.59.
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Pakistan vs Sri Lanka - 1st Test 4
SL 282/6 OVERS: 91.5
Australia vs New Zealand - 1st Test 3
AUS 26/0 OVERS: 13.3
NZ 166 (55.2 Ovs)
AUS lead by 276 runs
USA 144/5 OVERS: 34.1
India vs West Indies - 1st ODI
15 Dec, 2019 13:30 IST
MA Chidambaram Stadium, Chennai
United Arab Emirates vs Scotland - Match 6
15 Dec, 2019 11:30 IST | 06:00 GMT
ICC Academy, Dubai
India vs West Indies - 1st ODI
15 Dec, 2019 13:30 IST | 08:00 GMT
MA Chidambaram Stadium, Chennai
India vs West Indies - 2nd ODI
18 Dec, 2019 13:30 IST | 08:00 GMT
Dr. Y.S. Rajasekhara Reddy ACA-VDCA Cricket Stadium, Visakhapatnam
Pakistan vs Sri Lanka - 2nd Test
19 Dec, 2019 10:15 IST | 04:45 GMT
National Stadium, Karachi
India vs West Indies - 3rd ODI
22 Dec, 2019 13:30 IST | 08:00 GMT
Barabati Stadium, Cuttack
United Arab Emirates vs USA - Match 4
USA beat United Arab Emirates by 98 runs
India vs West Indies - 3rd T20I
India beat West Indies by 67 runs
USA beat Scotland by 35 runs
Nepal vs Maldives - 3rd Place Play-off
Nepal beat Maldives by 5 wickets
Bangladesh Under-23 vs Sri Lanka Under-23 - Final
Match over