Equation 677 Database

Magma ee91772f0657…

magma ee91772f0657
Size
841
Isomorphism class hash
ee91772f06572f92f169bfc2282dae2327f52fa3b4914b2d581f54c44f2ea9af
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
dwrensha
Submitted at
2026-05-20 19:22:22
Display reorder
838,839,804,559,802,205,100,52,472,171,81,153,110,242,201,239,614,38,192,92,725,522,713,672,678,767,327,285,760,465,674,367,652,508,758,780,46,630,661,821,333,395,284,675,426,437,39,717,744,538,445,252,827,621,255,488,623,384,244,718,808,57,206,492,765,70,212,730,290,175,115,97,332,772,158,197,737,529,86,43,683,774,141,619,677,809,477,126,417,552,31,798,259,358,711,183,215,521,32,35,573,530,140,84,781,271,360,714,579,494,403,119,510,443,664,526,697,71,317,232,828,604,549,82,90,703,161,757,135,750,229,794,182,195,512,462,668,143,310,191,829,63,792,715,42,258,321,399,595,313,570,302,238,571,612,78,144,736,226,184,484,9,142,330,15,334,481,406,286,366,638,112,133,424,393,511,433,563,116,74,21,350,383,519,240,500,60,551,165,542,261,249,569,208,109,22,654,555,407,771,788,704,701,547,659,398,355,170,27,706,26,556,114,709,79,65,178,793,121,505,574,776,568,210,254,412,438,524,266,525,516,353,545,230,778,541,418,251,588,198,11,644,509,796,50,726,532,423,594,99,12,373,397,490,729,155,501,274,106,134,375,473,558,695,650,352,275,764,304,66,694,606,702,415,800,485,812,59,318,743,369,272,422,806,493,608,430,446,646,637,518,596,436,790,463,49,640,359,754,831,684,420,405,662,837,685,768,265,447,56,598,727,636,475,548,343,377,262,294,489,411,263,243,189,486,429,307,231,339,138,575,741,20,117,283,149,335,643,600,83,147,371,404,617,14,291,326,576,582,23,587,835,572,666,825,830,815,8,33,671,840,810,567,577,676,691,686,805,3,696,18,592,13,681,562,28,820,773,129,150,368,453,791,193,536,370,496,392,589,45,6,413,540,269,520,94,721,639,246,225,136,724,7,527,504,583,347,710,186,457,789,752,77,227,37,824,698,177,130,85,823,692,58,173,190,745,733,599,101,787,305,507,224,156,544,799,280,667,87,234,148,47,554,755,673,720,609,105,467,797,833,762,517,68,237,166,200,834,322,708,187,196,76,95,288,376,459,312,122,152,581,434,25,88,331,456,746,605,296,194,580,648,19,213,108,340,622,268,344,154,409,416,236,311,103,137,216,248,34,620,5,292,396,602,663,761,449,474,389,320,560,471,561,356,169,123,209,346,167,303,324,228,132,319,204,591,419,658,0,211,223,341,351,315,756,287,278,306,162,164,590,444,391,29,98,298,118,466,469,597,615,145,499,131,716,535,584,531,363,578,719,634,264,40,365,448,803,2,276,515,1,491,786,124,557,220,89,408,387,188,690,641,523,364,807,732,299,645,632,603,267,54,410,61,382,468,425,452,348,795,689,270,553,441,836,738,480,601,759,394,128,281,10,479,174,233,625,454,361,329,4,766,566,308,253,633,476,172,221,607,565,316,107,401,325,179,73,297,362,618,822,739,421,328,41,647,379,616,533,432,390,660,503,460,250,440,69,314,656,753,669,483,247,712,670,816,775,777,688,214,75,337,48,482,735,102,91,814,497,120,534,682,176,180,742,624,62,295,202,146,813,700,163,779,723,217,817,811,478,309,455,427,642,769,770,277,651,245,385,374,451,357,707,748,435,655,611,323,613,665,699,64,498,528,36,199,627,293,439,301,345,241,586,610,113,386,157,751,218,414,127,461,24,159,282,336,653,349,464,93,585,273,381,30,181,151,782,740,687,207,222,487,539,300,728,53,125,67,784,342,502,629,168,80,819,747,705,219,96,185,818,693,72,431,257,470,51,680,450,354,785,289,543,628,763,400,749,458,513,338,722,260,657,826,44,626,372,631,442,832,679,635,428,734,550,203,537,495,380,593,731,402,139,256,55,378,111,388,801,17,279,546,514,104,506,783,649,564,160,235,16 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

F_29² Type-1 affine line magma at size 841. Size 841 = 29², fully idempotent, RC. Linear over the extension field F_29² = F_29[α]/⟨α² − 2⟩. Operation: x ◇ y = (1−β)·x + β·y in F_29², with β a primitive 10th root of unity in F_29² (= root of Phi_10(x) = x⁴ − x³ + x² − x + 1). F_29² has |F_29²*| = 840 = 2³·3·5·7, divisible by 10, so 4 primitive 10th roots exist; up to Galois conjugacy these form 2 orbits of 2, giving 2 distinct iso classes at size 841 (this magma corresponds to one of the two Galois orbits; the other is magma#cc0cd58750be). This is the "AG(2, 29) affine line over F_29²" magma. Sub-magma structure: NO size-29 sub-magmas (since the Phi_10 root β lies in F_29² \ F_29, the F_29 prime subfield is not preserved by the operation). Every pair of distinct elements generates the full 841-element magma. Companion to the other F_29² linear magmas at size 841 in the DB: magma#cc0cd58750be (the other Type-1 iso class) and the two Type-2 magmas magma#8469938fe79d, magma#630bb9976070 (Phi_2_5-root constructions). The size-841 family also includes magma#ad16fb07 (an exceptional non-standard construction, possibly the Zassenhaus near-field of order 841) and various other entries — see size-841 page commentary. [text written by Claude]

last edited by dwrensha at 2026-05-20 19:28:51 · history