subquery with group by not using index

CREATE TABLE `t1` (

	`id` INT(11) NOT NULL,

	`amt` INT(11) NULL DEFAULT NULL,

	PRIMARY KEY (`id`),

	INDEX `amt` (`amt`)

);

CREATE TABLE `t2` (

	`amt` INT(11) NOT NULL,

	`somestring` VARCHAR(50) NULL DEFAULT NULL COLLATE 'utf8_unicode_ci',

	INDEX `amt_ind` (`amt`)

);

INSERT INTO `t2` (`amt`, `somestring`) VALUES (4, 'AtcsBD');

INSERT INTO `t2` (`amt`, `somestring`) VALUES (3, 'Wqjovg');

INSERT INTO `t2` (`amt`, `somestring`) VALUES (2, 'iWjoMy');

INSERT INTO `t2` (`amt`, `somestring`) VALUES (3, 'eoAkem');

INSERT INTO `t2` (`amt`, `somestring`) VALUES (4, '23Dj9r');

INSERT INTO `t2` (`amt`, `somestring`) VALUES (1, 'Im42UO');

INSERT INTO `t2` (`amt`, `somestring`) VALUES (1, 'qbjV4X');

INSERT INTO `t2` (`amt`, `somestring`) VALUES (1, 'BuO8oI');

INSERT INTO `t2` (`amt`, `somestring`) VALUES (2, '6Lf5Fv');

INSERT INTO `t2` (`amt`, `somestring`) VALUES (1, 'udFOm8');

INSERT INTO `t1` (`id`, `amt`) VALUES (2, 1);

INSERT INTO `t1` (`id`, `amt`) VALUES (3, 1);

INSERT INTO `t1` (`id`, `amt`) VALUES (7, 1);

INSERT INTO `t1` (`id`, `amt`) VALUES (10, 1);

INSERT INTO `t1` (`id`, `amt`) VALUES (1, 2);

INSERT INTO `t1` (`id`, `amt`) VALUES (4, 2);

INSERT INTO `t1` (`id`, `amt`) VALUES (5, 2);

INSERT INTO `t1` (`id`, `amt`) VALUES (9, 2);

INSERT INTO `t1` (`id`, `amt`) VALUES (6, 3);

INSERT INTO `t1` (`id`, `amt`) VALUES (8, 3);

explain

select *

from t1 a

inner join 

(select * from t2 group by amt) b

 on a.amt = b.amt 

where b.amt = 1;

MariaDB [bughunt]> explain select * from t1 a inner join  (select * from t2 group by amt) b  on a.amt = b.amt  where a.amt = 1 \G

*************************** 1. row ***************************

           id: 1

  select_type: PRIMARY

        table: a

         type: ref

possible_keys: amt

          key: amt

      key_len: 5

          ref: const

         rows: 4

        Extra: Using index

*************************** 2. row ***************************

           id: 1

  select_type: PRIMARY

        table: <derived2>

         type: ALL

possible_keys: NULL

          key: NULL

      key_len: NULL

          ref: NULL

         rows: 4

        Extra: Using where; Using join buffer (flat, BNL join)

*************************** 3. row ***************************

           id: 2

  select_type: DERIVED

        table: t2

         type: ALL

possible_keys: amt_ind

          key: NULL

      key_len: NULL

          ref: NULL

         rows: 10

        Extra: Using where

3 rows in set (0.00 sec)

}