Equation 677 Database

Magma cc0cd58750be…

magma cc0cd58750be
Size
841
Isomorphism class hash
cc0cd58750beea3d84d4a9b7c9fe98e32dbc56f7badc5df665772e5c4a63b188
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
dwrensha
Submitted at
2026-05-20 19:20:58
Display reorder
838,839,769,198,573,776,817,697,62,735,664,129,412,585,401,318,301,213,58,426,429,103,767,72,385,678,567,259,655,319,197,532,661,539,169,458,262,337,571,85,708,236,275,150,131,531,422,325,510,373,206,36,25,624,369,711,420,9,523,533,775,840,810,498,558,805,825,795,780,493,785,513,508,553,835,538,503,800,518,543,548,820,528,815,830,790,770,423,204,504,696,497,162,284,44,455,746,404,589,60,1,171,408,545,290,457,496,96,185,240,271,743,120,606,302,227,782,811,608,163,734,804,803,690,224,602,643,350,107,732,138,464,461,23,248,336,283,366,620,377,94,699,700,27,662,801,356,97,153,367,128,794,689,451,680,17,238,592,772,343,410,598,610,722,724,84,454,793,760,13,214,652,326,633,738,285,399,691,115,452,584,492,601,491,55,157,297,91,66,349,222,180,166,39,488,235,403,450,199,266,540,741,499,186,111,621,641,761,353,200,317,512,419,490,255,242,177,604,305,216,438,299,5,472,758,149,59,16,511,135,519,470,345,225,287,681,440,56,442,256,212,552,731,156,551,728,478,147,389,393,81,105,189,339,574,530,170,591,559,29,45,378,629,14,666,267,713,136,515,30,425,537,463,90,155,330,41,716,202,174,576,210,427,141,374,324,544,342,241,536,89,18,638,158,694,243,415,729,765,331,102,799,22,348,727,798,657,361,133,685,777,615,459,219,806,372,456,597,603,215,329,541,671,520,468,46,581,379,246,19,71,542,335,179,146,347,564,718,430,160,207,432,549,383,272,35,95,721,83,298,715,178,617,479,381,42,749,658,476,565,677,819,365,38,392,797,818,122,263,109,826,635,747,281,644,623,239,742,792,471,173,346,813,560,612,639,117,672,474,618,258,814,376,234,104,360,37,78,821,33,744,293,630,387,653,710,8,605,12,148,279,717,233,362,647,719,587,123,321,79,837,789,698,449,338,684,796,788,405,446,351,755,593,675,92,187,196,226,651,15,140,159,359,521,252,480,315,561,309,363,768,522,26,265,529,614,121,448,701,482,327,69,500,75,434,390,660,203,632,134,323,431,77,264,704,822,669,406,63,702,572,774,781,740,590,218,108,683,773,578,67,417,306,288,99,667,168,695,355,469,341,382,32,613,808,648,73,253,625,705,816,809,607,737,28,371,634,787,739,229,112,466,194,175,50,686,261,161,152,110,535,34,292,447,736,483,86,579,494,230,61,557,733,398,344,596,280,445,217,556,394,268,752,244,183,47,570,43,127,640,628,720,386,481,370,823,831,649,303,484,663,824,802,114,286,88,622,754,682,397,595,778,311,208,436,827,707,745,688,352,665,328,709,68,786,113,2,395,139,269,411,779,223,583,439,637,82,674,577,416,444,582,143,750,333,118,274,588,679,316,712,670,791,74,228,87,783,832,357,3,400,784,642,600,441,693,714,7,11,433,555,636,506,294,250,756,130,0,237,418,514,467,172,195,465,753,599,312,181,144,300,507,106,54,211,414,616,380,278,659,193,673,53,124,568,562,421,407,771,254,424,580,812,650,98,396,692,833,762,313,57,834,137,296,730,764,101,748,232,631,49,594,413,501,276,307,509,289,409,176,462,245,611,209,167,751,6,295,190,125,428,502,460,65,550,477,21,475,646,322,260,310,10,64,524,626,205,495,609,304,154,70,116,358,354,182,443,763,516,191,766,517,247,221,165,388,726,676,586,76,151,435,554,100,546,51,24,184,723,437,40,334,473,251,340,569,142,277,220,525,384,547,282,619,487,80,656,364,320,703,534,706,505,231,164,485,368,270,453,4,201,145,257,314,31,126,332,192,20,526,566,527,829,93,402,188,132,391,836,668,291,687,249,48,725,828,489,119,759,757,575,563,375,308,807,627,273,52,645,486,654 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#ee91772f0657). 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 19:28:50 · history