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 A211171 Exponent of general linear group GL(n,2). 1
 1, 6, 84, 420, 26040, 78120, 9921240, 168661080, 24624517680, 270869694480, 554470264600560, 7208113439807280, 59041657185461430480, 2538791258974841510640, 383357480105201068106640, 98522872387036674503406480, 25826982813282567927671981480160 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the smallest integer for which x^a(n) = 1 for any x in GL(n,2). LINKS Alexander Gruber, Table of n, a(n) for n = 1..100 StackExchange thread on the exponent of GL(n,q) FORMULA a(n) = 2^ceiling(Log_2(n)) * ( product from k=1 to n of the k-th cyclotomic polynomial evaluated at 2 ). EXAMPLE n = 2: GL(2,2) is isomorphic to S3 which has exponent 6 (see: A003418). n = 3: The set of element orders of GL(3,2) is {1,2,3,4,7} so the exponent is 84. n = 5: The set of element orders of GL(5,2) is {1,2,3,4,5, 6,7,8,12,14, 15,21,31} so the exponent is 26040 (see: A053651). MAPLE with(numtheory): a:= proc(n) local t; t:= 2^ilog2(n);       `if`(t

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)