Equation 677 Database

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Magma ad16fb07e4c3…

magma ad16fb07e4c3
Size
841
Isomorphism class hash
ad16fb07e4c35cac3d07e2f16567bdc4ecd101447386c42678c456082914cdd1
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-14 05:12:21
Display reorder
0,1,463,668,594,538,133,69,840,63,86,520,563,638,462,29,8,815,658,284,433,273,801,30,315,183,482,792,40,62,22,830,701,663,224,285,793,7,15,240,84,821,134,643,93,823,101,244,20,41,800,293,233,673,712,772,49,48,55,808,485,145,334,50,822,225,470,308,683,771,21,2,176,487,458,408,309,266,36,837,181,707,536,569,131,672,38,291,558,791,272,490,572,831,528,755,584,112,785,78,301,116,401,465,762,221,508,675,248,540,634,313,639,380,706,152,99,637,68,34,636,467,576,747,450,174,773,307,756,360,384,573,184,114,254,625,488,177,325,32,779,3,719,522,810,735,796,596,429,109,627,219,486,451,533,381,783,97,753,67,426,124,655,602,629,744,702,585,331,173,489,553,354,725,550,368,355,424,591,103,819,106,700,399,249,496,238,494,327,836,236,827,321,575,290,758,275,506,386,121,654,155,393,689,344,412,318,652,686,258,657,4,835,182,392,209,268,98,674,685,107,76,319,502,137,621,624,443,353,179,765,811,111,546,336,697,588,818,201,557,631,239,66,670,526,383,438,457,159,789,542,260,215,605,409,839,298,263,297,750,312,447,214,704,681,366,295,400,466,577,724,208,578,80,142,529,480,543,703,743,186,5,127,352,162,834,35,456,713,246,161,648,351,421,774,516,693,509,541,730,519,10,251,342,464,481,25,341,809,262,469,65,708,595,734,100,45,570,122,337,414,633,474,316,616,144,60,799,571,517,347,698,512,241,306,217,653,207,709,373,587,688,154,166,592,705,678,125,252,135,132,6,64,661,118,620,136,746,667,58,247,395,165,679,269,317,294,782,739,628,662,18,778,211,52,531,88,81,549,153,650,816,330,556,761,539,445,415,527,430,391,812,12,292,185,760,205,598,157,245,814,448,579,237,427,387,613,442,763,139,532,203,243,454,780,644,599,89,394,722,326,9,422,188,589,559,333,33,56,37,764,766,288,500,741,232,23,108,732,305,642,564,498,94,323,607,223,61,47,71,651,255,375,220,483,85,455,300,478,535,194,113,274,175,229,601,198,104,19,28,286,339,525,410,350,684,42,14,218,200,728,385,163,314,51,665,523,583,432,265,441,11,27,794,222,826,170,503,102,434,43,477,618,358,610,608,338,781,115,388,370,304,833,691,72,59,91,310,364,612,126,807,16,680,476,515,574,158,501,322,838,721,83,461,497,752,193,423,547,204,820,54,348,586,676,299,795,195,664,660,168,513,716,261,687,335,742,717,376,382,711,13,786,505,367,196,180,751,253,484,749,767,614,604,733,692,802,530,777,120,287,770,26,57,226,369,228,788,757,146,829,44,190,405,499,444,495,593,31,690,407,453,39,440,646,471,123,493,178,659,635,210,79,775,403,371,518,270,603,346,666,609,264,813,92,192,568,475,259,745,105,17,77,435,562,199,817,417,234,723,267,329,784,340,277,197,790,187,803,590,372,452,332,437,754,694,623,567,140,406,626,160,682,53,231,759,390,363,736,710,130,420,699,510,379,439,320,600,143,647,641,806,748,473,630,720,343,374,289,171,361,548,70,787,87,82,250,581,278,95,565,24,545,560,615,632,129,96,669,695,151,283,46,645,768,402,345,280,362,521,167,324,460,191,622,552,365,731,804,413,656,727,832,216,671,524,150,737,359,479,740,828,349,561,544,271,468,138,164,212,611,279,328,537,206,110,73,230,504,147,436,425,119,449,824,582,825,213,714,416,491,74,172,718,149,311,726,617,276,554,227,303,257,202,696,169,776,281,396,411,156,128,534,282,597,75,805,507,446,302,398,148,431,566,511,459,472,377,397,389,492,619,117,715,256,357,235,141,242,90,606,797,378,514,729,677,428,769,189,418,419,798,649,640,580,551,555,356,404,296,738 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-841 = 29² idempotent right-cancellative magma — non-standard linear construction. Size 841, fully idempotent, RC. L_0 cycle 1 + 84·10 (left-multiplier has order 10 — consistent with a Phi_10-related multiplier). R_0 cycle 1 + 12·70 (right-multiplier has order 70). Verified NOT to be: - F_29² Type-1 linear magma (= AG(2, 29) affine line). All 4 primitive 10th roots in F_29² give 2 distinct iso classes magma#cc0cd58750be and magma#ee91772f0657, neither matching this magma. - F_29² Type-2 linear magma. All 4 Phi_2_5 roots in F_29² give 2 distinct iso classes magma#8469938fe79d and magma#630bb9976070 (both non-fully-idempotent), neither matching this magma. So this is likely either: - The Zassenhaus exceptional near-field of order 29² = 841 (Zassenhaus near-fields exist at p² for p ∈ {5, 7, 11, 23, 29, 59}). The Zassenhaus near-field of order 841 has multiplicative group of order 840. - A "twisted AG(2, 29)" magma with only some of the 30 parallel classes preserved as sub-magmas (analog of the 2-class / 4-class / 8-class twisted AG(2, 11) family at size 121). Determining the exact construction would require deeper analysis: enumerating size-29 sub-magmas (currently expensive due to size 841), or computing |Aut| and comparing to expected automorphism orders for each candidate construction. [text written by Claude]

last edited by dwrensha at 2026-05-20 19:28:50 · history