The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A058502

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Number of cyclic subgroups of Chevalley group A_n(3) (the group of nonsingular n X n matrices over GF(3)).
(history; published version)

#9 by Michael De Vlieger at Sun Aug 07 07:50:26 EDT 2022

STATUS

reviewed

approved

#8 by Michel Marcus at Sun Aug 07 05:42:35 EDT 2022

STATUS

proposed

reviewed

#7 by Sean A. Irvine at Sun Aug 07 05:42:19 EDT 2022

STATUS

editing

proposed

#6 by Sean A. Irvine at Sun Aug 07 05:42:16 EDT 2022

FORMULA

a(n) = Sum_{d} |{g element of A_n(3): order(g)=d}| / phi(d), where phi is the Euler totient function. - Sean A. Irvine, Aug 07 2022

STATUS

proposed

editing

#5 by Sean A. Irvine at Sun Aug 07 00:00:49 EDT 2022

STATUS

editing

proposed

Discussion

Sun Aug 07

02:02

Michel Marcus: is there a formula ?

05:09

Sean A. Irvine: It's like the one in A062250 -- although to actually compute you can't really search through d, instead do something based on the cycle index of GL(GF(3)) as per code.

#4 by Sean A. Irvine at Sun Aug 07 00:00:26 EDT 2022

NAME

Number of cyclic subgroups of Chevalley group A_n(3) (the group of nonsingular n X n matrices over GF(3) ).

DATA

2, 28, 3592, 4375990, 45881030476, 4761512868259322, 4226568802536503453172, 4761512868259324, 4226568802536503453176, 33913358590726454284540553032, 2539147871121449320978174414096629904, 1751590210907807486213696422942566723118774192, 10257642878603441540313639499316772578643776243183698528

LINKS

Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a058/A058502.java">Java program</a> (github)

EXTENSIONS

a(6)-a(7) corrected and more terms from Sean A. Irvine, Aug 07 2022

STATUS

approved

editing

#3 by Charles R Greathouse IV at Fri May 10 12:44:33 EDT 2013

EXTENSIONS

More terms from _Vladeta Jovovic (vladeta(AT)eunet.rs), _, Jul 05 2001

Discussion

Fri May 10

12:44

OEIS Server: https://oeis.org/edit/global/1911

#2 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

KEYWORD

nonn,new

nonn

EXTENSIONS

More terms from Vladeta Jovovic (vladeta(AT)Euneteunet.yurs), Jul 05 2001

#1 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

NAME

Number of cyclic subgroups of Chevalley group A_n(3) (the group of nonsingular n X n matrices over GF(3) ).

DATA

2, 28, 3592, 4375990, 45881030476, 4761512868259322, 4226568802536503453172, 33913358590726454284540553032, 2539147871121449320978174414096629904

OFFSET

1,1

CROSSREFS

Cf. A053658 (unlabeled case), A062250, A062552, A053290.

KEYWORD

nonn

AUTHOR

Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 02 2001

EXTENSIONS

More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 05 2001

STATUS

approved