A334994 Orders of the groups PSL(m,q) in increasing order as q runs through the prime powers (without repetitions).

6, 12, 60, 168, 360, 504, 660, 1092, 2448, 3420, 4080, 5616, 6072, 7800, 9828, 12180, 14880, 20160, 25308, 32736, 34440, 39732, 51888, 58800, 74412, 102660, 113460, 150348, 178920, 194472, 246480, 262080, 265680, 285852, 352440, 372000, 456288, 515100, 546312

Offset: 1

Author

Michel Marcus, May 19 2020

Keywords

• nonn

Comments

60 is the order of PSL(2,4) or PSL(2,5).

168 is the order of PSL(2,7) or PSL(3,2).

20160 is the order of PSL(4,2) or PSL(3,4).

See A334884 and A335000 for variations of this sequence.

Examples

			#PSL(2,7) = (7^2-1)*7/gcd(2,6) = 168 = a(4), and,
#PSL(3,2) = (2^3-1)*(2^3-2)*2^2/gcd(3,1) = 168 = a(4).
		

Links

• Wikipedia, Projective linear group
• Index entries for sequences related to groups.

Crossrefs

Cf. A117762 (PSL(2, prime(n))).

Cf. A334884 and A335000 (both with repetitions, but different).

Formula

#PSL(m,q) = (Product_{j=0..m-2} (q^m - q^j)) * q^(m-1) / gcd(m,q-1). - Bernard Schott, May 19 2020