A335000 Orders of the groups PSL(m,q) in increasing order as q runs through the prime powers (with repetitions).

6, 12, 60, 60, 168, 168, 360, 504, 660, 1092, 2448, 3420, 4080, 5616, 6072, 7800, 9828, 12180, 14880, 20160, 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) and of PSL(2,5).

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

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

Other repetitions > 20160 for PSL(m,q) groups are not known.

See A334884 and A334994 for variations of this sequence.

Examples

			a(5) = #PSL(2,7) = (7^2-1)*7/gcd(2,6) = 168, and,
a(6) = #PSL(3,2) = (2^3-1)*(2^3-2)*2^2/gcd(3,1) = 168.
		

Links

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

Crossrefs

Cf. A002884 \ {1} (PSL(n,2)), A117762 (PSL(2, prime(n))).

Cf. A334884 (another case with repetitions), A334994 (without repetitions).

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