loop ... ...
0 members (0 subcategories, 0 files) - 18:25, 24 February 2011
==Statement==
It is possible to have a finite loop such that the exponent of the loop does not divide the order of the loop.
==Proof== ... ...
395 bytes (66 words) - 15:46, 26 June 2012
#redirect Moufang loops of order 48 ... ...
39 bytes (5 words) - 13:58, 20 August 2011
#redirect Moufang loops of order 81 ... ...
39 bytes (5 words) - 12:47, 20 August 2011
#redirect Moufang loops of order 16 ... ...
39 bytes (5 words) - 07:19, 20 August 2011
#redirect Moufang loops of order 32 ... ...
39 bytes (5 words) - 07:21, 20 August 2011
#redirect Characteristic not implies normal in algebra loops ... ...
64 bytes (8 words) - 15:09, 25 July 2009
#redirect Moufang loops of order 48 ... ...
39 bytes (5 words) - 13:59, 20 August 2011
#redirect Moufang loops of order 24 ... ...
39 bytes (5 words) - 13:57, 20 August 2011
! Quantity !! Value for groups !! Value for Moufang loops that are ... To understand these in a broader context, see Moufang loops of order ... ...
692 bytes (89 words) - 13:36, 20 August 2011
#redirect Moufang loops of order 81 ... ...
39 bytes (5 words) - 12:46, 20 August 2011
! Quantity !! Value for groups !! Value for Moufang loops that are ... To understand these in a broader context, see Moufang loops of order ... ...
877 bytes (111 words) - 12:45, 20 August 2011
! Quantity !! Value for groups !! Value for Moufang loops that are ... This article concentrates on the Moufang loops of order 32 that are ... ...
912 bytes (122 words) - 12:20, 20 August 2011
This article describes the Moufang loops of order 16. There is a total of 19 Moufang loops up to isomorphism. Of these, 14 are groups, and these ... ...
789 bytes (99 words) - 12:12, 20 August 2011
#redirect Moufang loops of order 64 ... ...
39 bytes (5 words) - 07:24, 20 August 2011
#redirect Moufang loops of order 32 ... ...
39 bytes (5 words) - 07:20, 20 August 2011
#redirect Moufang loops of order 16 ... ...
39 bytes (5 words) - 07:19, 20 August 2011
#redirect Moufang loops of order 3.2^n ... ...
42 bytes (6 words) - 03:01, 20 August 2011
#redirect Moufang loops of order 2^n ... ...
40 bytes (6 words) - 02:46, 20 August 2011
==Statement==
===Verbal statement===
A characteristic subloop of a loop need not be a normal subloop.
==Related facts==
* Normal implies Lagrange-like ... ...
1 KB (168 words) - 06:10, 21 August 2011
a complete list of particular loops ... ...
172 bytes (25 words) - 18:24, 24 February 2011
This article describes the Moufang loops of order 16. There is a total of 19 Moufang loops up to isomorphism. Of these, 14 are groups, and these ... ...
789 bytes (99 words) - 12:12, 20 August 2011
==Number of Moufang loops of small orders==
{| class="sortable" border="1"
! Exponent n !! Value 2^n !! Number of groups of ... ...
1 KB (133 words) - 02:52, 20 August 2011
! Quantity !! Value for groups !! Value for Moufang loops that are ... This article concentrates on the Moufang loops of order 32 that are ... ...
912 bytes (122 words) - 12:20, 20 August 2011
! Quantity !! Value for groups !! Value for Moufang loops that are ... To understand these in a broader context, see Moufang loops of order ... ...
692 bytes (89 words) - 13:36, 20 August 2011
==Number of Moufang loops of small orders==
{| class="sortable" border="1"
! Exponent n !! Value 2^n !! Value 3 \cdot 2^n ... ...
1,022 bytes (132 words) - 08:57, 5 June 2023
! Quantity !! Value for groups !! Value for Moufang loops that are ... To understand these in a broader context, see Moufang loops of order ... ...
877 bytes (111 words) - 12:45, 20 August 2011
* Sylow subloops exist for Sylow primes in finite Moufang loops * 3-Sylow subloops exist in finite Moufang loops
* Sylow subloops exist ... ...
916 bytes (142 words) - 07:42, 20 August 2011
#redirect Moufang loops of order 16 ... ...
39 bytes (5 words) - 07:19, 20 August 2011
#redirect Moufang loops of order 16 ... ...
39 bytes (5 words) - 07:19, 20 August 2011
#redirect Moufang loops of order 81 ... ...
39 bytes (5 words) - 12:46, 20 August 2011
#redirect Moufang loops of order 81 ... ...
39 bytes (5 words) - 12:47, 20 August 2011
#redirect Moufang loops of order 24 ... ...
39 bytes (5 words) - 13:57, 20 August 2011
#redirect Moufang loops of order 48 ... ...
39 bytes (5 words) - 13:58, 20 August 2011
#redirect Moufang loops of order 48 ... ...
39 bytes (5 words) - 13:59, 20 August 2011
#redirect Moufang loops of order 64 ... ...
39 bytes (5 words) - 07:24, 20 August 2011
#redirect Moufang loops of order 32 ... ...
39 bytes (5 words) - 07:21, 20 August 2011
#redirect Moufang loops of order 32 ... ...
39 bytes (5 words) - 07:20, 20 August 2011
#redirect Moufang loops of order 3.2^n ... ...
42 bytes (6 words) - 03:01, 20 August 2011
#redirect Characteristic not implies normal in algebra loops ... ...
64 bytes (8 words) - 15:09, 25 July 2009