MySQL 5.5

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select version();


version()


5.5.62


CREATE TABLE table1 (`Type` char(1), `rank` INTEGER);
INSERT INTO table1 values
('A',1), ('A',2), ('B',3), ('A',4), 
('B',5), ('B',6), ('B',7), ('A',8);
select type, bucket, max(rank) as maxRank from (
  select `type`, rank, 
    @bucket := @bucket + if(`type` = @curr, 0, 1) as bucket,
    @curr := `type`
  from table1
  join (select @curr:='', @bucket:=0) v
  order by rank
) t group by bucket


type
bucket
maxRank


A
1
2

B
2
3

A
3
4

B
4
7

A
5
8


set @curr:='', @bucket:=0;

select type, bucket, max(rank) as maxRank from (
  select `type`, rank, 
    @bucket := @bucket + if(`type` = @curr, 0, 1) as bucket,
    @curr := `type`
  from table1
  order by rank
) t group by bucket


type
bucket
maxRank


A
1
2

B
2
3

A
3
4

B
4
7

A
5
8