The On-Line Encyclopedia of Integer Sequences (OEIS)

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A329119

Orders of the finite groups SL_2(K) when K is a finite field with q = A246655(n) elements.
(history; published version)

#37 by Michael De Vlieger at Mon Apr 04 10:21:04 EDT 2022

STATUS

reviewed

approved

#36 by Joerg Arndt at Mon Apr 04 09:51:58 EDT 2022

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proposed

reviewed

#35 by Jianing Song at Mon Apr 04 09:35:06 EDT 2022

STATUS

editing

proposed

#34 by Jianing Song at Mon Apr 04 09:34:48 EDT 2022

COMMENTS

Also a(n) is the order of PGL_2(K) when K is a finite field with q = A246655(n) elements. Note that PGL(m,q) and SL(m,q) are not isomorphic unless gcd(m,q-1) = 1. For example, PGL(2,3) = S_4 is not isomorphic to SL(2,3), PGL(2,5) = S_5 is not isomorphic to SL(2,5). - Jianing Song, Apr 04 2022

LINKS

Groupprops, <a href="https://groupprops.subwiki.org/wiki/Projective_general_linear_group_of_degree_two">Projective general linear group of degree two</a>

Groupprops, <a href="https://groupprops.subwiki.org/wiki/Special_linear_group_of_degree_two">Special linear group of degree two</a>

#33 by Jianing Song at Mon Apr 04 06:26:47 EDT 2022

COMMENTS

Also order of PGL_2(K). Note that PGL(m,q) and SL(m,q) are not isomorphic for unless gcd(m >= 2 and ,q not a power of 2-1) = 1. For example, PGL(2,3) = S_4 is not isomorphic to SL(2,3), PGL(2,5) = S_5 is not isomorphic to SL(2,5). - Jianing Song, Apr 04 2022

#32 by Jianing Song at Mon Apr 04 01:23:47 EDT 2022

COMMENTS

Also order of PGL_2(K). Note that PGL(m,q) and SL(m,q) are not isomorphic for m >= 2 and q not a power of 2. For example, PGL(2,3) = S_4 is not isomorphic to SL(2,3), PGL(2,5) = S_5 is not isomorphic to SL(2,5). - _Jianing Song_, Apr 04 2022

#31 by Jianing Song at Mon Apr 04 01:05:13 EDT 2022

COMMENTS

Also order of PGL_2(K)

STATUS

approved

editing

#30 by Andrew Howroyd at Sat Aug 22 17:43:40 EDT 2020

STATUS

reviewed

approved

#29 by Amiram Eldar at Sat Aug 22 16:11:17 EDT 2020

STATUS

proposed

reviewed

#28 by Jean-François Alcover at Sat Aug 22 02:56:02 EDT 2020

STATUS

editing

proposed