Equation 677 Database

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Magma 630bb9976070…

magma 630bb9976070
Size
841
Isomorphism class hash
630bb9976070344e98c9999a26a945327c3751915ba5457360e4ea3e91dda33d
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Submitted by
dwrensha
Submitted at
2026-05-20 19:25:12
Display reorder
840,836,581,821,746,686,566,716,491,806,431,761,731,446,461,671,656,521,551,641,596,701,506,776,476,536,611,791,626,376,479,134,496,239,750,663,147,595,40,168,212,135,755,688,534,797,57,265,249,166,777,175,649,652,32,426,101,773,46,699,644,542,33,297,661,125,404,414,495,216,828,522,15,225,760,814,356,817,218,348,262,591,34,268,500,518,433,361,153,151,464,197,762,119,120,160,481,740,634,224,673,637,735,519,93,648,782,831,132,42,203,580,250,758,25,234,286,390,444,505,809,559,707,99,349,562,157,383,826,208,24,122,74,756,84,350,660,128,381,665,573,683,687,598,362,226,513,290,113,502,749,302,605,214,148,289,445,538,321,696,766,156,804,627,373,204,323,647,330,623,600,367,402,499,104,480,21,684,19,333,629,813,247,527,507,576,94,31,95,282,6,253,646,745,485,415,799,503,389,341,838,399,802,256,178,657,127,635,186,630,779,726,360,70,568,353,543,319,403,529,54,834,397,332,796,653,532,351,677,320,475,44,146,97,60,314,609,501,670,324,554,210,724,825,452,27,266,51,209,830,727,738,3,428,53,432,571,763,258,105,340,346,725,816,138,619,117,136,5,100,449,658,188,182,622,565,747,720,235,409,504,743,410,78,86,145,633,219,466,767,391,511,678,2,150,549,280,792,667,43,494,254,162,183,770,812,264,190,16,788,149,765,610,110,703,72,181,664,441,301,520,722,577,421,137,23,143,588,613,405,824,41,172,106,89,365,396,698,377,459,574,364,398,39,771,675,680,702,271,142,645,375,368,418,429,811,366,490,193,650,794,85,558,544,412,668,692,59,672,201,741,583,334,69,347,547,335,406,221,295,58,177,827,9,780,718,679,526,165,807,509,198,279,803,625,87,456,693,564,682,269,785,205,164,52,196,116,73,228,694,822,294,26,579,800,67,236,192,795,541,524,818,471,697,103,211,310,422,733,180,213,640,708,284,179,7,274,189,498,430,308,275,523,632,98,306,315,487,681,608,734,751,585,287,141,352,590,789,387,199,612,484,133,358,14,291,337,259,300,575,174,472,774,483,666,372,835,593,184,293,719,597,260,736,469,508,570,118,617,272,343,200,126,176,50,757,62,354,49,793,531,296,462,344,482,458,20,754,768,370,584,440,288,700,81,601,639,4,83,90,435,237,206,492,470,465,561,400,37,79,784,669,92,488,35,80,374,318,267,326,614,13,823,798,238,384,232,631,787,512,730,30,651,454,276,357,493,322,820,555,244,578,408,285,169,602,560,278,257,159,704,328,457,582,185,759,245,416,468,721,61,557,676,124,423,240,371,363,18,533,714,17,140,510,537,775,832,277,283,448,659,312,114,231,8,829,233,606,515,241,55,317,163,553,781,642,338,638,417,528,517,620,304,336,171,388,662,615,514,305,764,112,460,711,819,102,345,382,161,329,685,108,467,66,742,443,586,47,36,624,339,739,11,107,753,68,778,355,75,516,569,420,281,425,222,447,273,316,592,38,628,56,28,713,589,0,695,535,436,158,115,187,380,392,379,786,717,737,152,603,419,48,411,474,413,690,131,709,10,82,810,833,45,437,111,299,88,837,594,251,556,486,109,748,655,194,243,309,815,207,539,712,325,195,723,191,77,808,477,473,783,455,96,223,450,65,369,546,359,217,385,303,616,22,252,772,64,311,497,769,599,715,654,29,76,139,386,548,155,790,298,327,227,621,572,438,378,729,525,427,463,129,424,530,691,255,215,839,552,292,674,246,248,331,643,728,710,173,395,801,167,63,123,607,71,604,550,130,407,732,618,121,705,1,12,220,451,202,394,752,434,489,91,563,313,636,393,442,439,270,567,261,154,170,342,587,744,478,545,230,307,263,401,805,242,453,540,144,706,229,689 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

F_29² Type-2 linear magma at size 841 (non-fully-idempotent). Size 841 = 29², NOT fully idempotent (only 1 idempotent: the F_29² zero element), right-cancellative. Linear over the extension field F_29² = F_29[α]/⟨α² − 2⟩. Operation: x ◇ y = α_coef·x + β·y in F_29², with β a root of Phi_2_5(x) = x⁴ + x³ + 2x² + 2x + 1 and α_coef = -β³ − β − 1. This is Pace Nielsen's "Type 2" construction. Phi_2_5 has 4 roots in F_29², forming 2 Galois-conjugate orbits → 2 distinct iso classes at size 841 (this magma is one Galois orbit; the other is magma#8469938fe79d). Sub-magma structure: NO size-29 sub-magmas. Every pair of distinct elements generates the full 841-element magma. Companion to the F_29² Type-1 magmas at size 841: magma#cc0cd58750be and magma#ee91772f0657 (both fully idempotent). The 4 F_29² linear magmas at size 841 (2 Type-1 + 2 Type-2) cover the full Pace Nielsen classification at this size. The size-841 family also includes magma#ad16fb07 (an exceptional non-standard construction) and other entries — see size-841 page commentary. [text written by Claude]

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