Equation 677 Database

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Magma b6037f9aa3cd…

magma b6037f9aa3cd
Size
876
Isomorphism class hash
b6037f9aa3cd2397ddae223351ce674c25845e2c167ab818f9c4ab90200af8bd
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 875) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 15:27:39
Display reorder
834,447,601,325,438,388,19,492,86,662,239,448,240,602,326,439,374,20,493,87,649,449,241,603,327,440,375,21,494,88,650,604,242,450,328,441,376,22,495,89,651,228,605,451,329,442,377,23,496,90,652,229,591,452,330,443,378,24,497,91,653,230,592,453,316,444,379,25,498,92,654,231,593,454,317,445,380,26,499,93,655,232,594,455,318,446,381,27,500,94,656,233,595,456,319,432,382,28,501,95,657,234,596,457,320,433,383,14,502,96,658,235,597,458,321,434,384,15,503,97,659,236,598,459,322,435,385,16,504,98,660,237,599,460,323,436,386,17,505,99,661,238,600,461,324,437,387,18,819,818,820,824,821,822,823,736,696,697,737,698,695,735,759,744,745,758,850,857,840,864,861,825,866,868,829,846,369,187,567,79,644,429,55,579,483,713,370,714,188,568,80,645,430,56,580,484,371,715,189,569,81,646,431,57,581,485,190,716,372,570,82,647,418,43,582,486,717,191,373,571,83,648,419,44,583,487,718,192,360,572,84,635,420,45,584,488,719,193,361,573,85,636,421,46,585,489,720,194,362,574,72,637,422,47,586,490,721,195,363,575,73,638,423,48,587,491,722,196,364,562,74,639,424,49,588,477,723,197,365,563,75,640,425,50,589,478,724,198,366,564,76,641,426,51,590,479,725,199,367,565,77,642,427,52,576,480,726,186,368,566,78,643,428,53,577,481,796,770,776,783,765,785,778,54,578,482,741,740,739,738,814,815,813,812,811,816,817,760,754,755,761,855,843,854,851,858,826,839,831,827,863,677,624,216,9,143,67,278,113,410,701,678,702,625,217,10,144,68,279,114,411,679,703,626,218,11,145,69,280,100,412,627,704,680,219,12,146,70,281,101,413,705,628,681,220,13,147,71,282,102,414,706,629,682,221,1,148,58,283,103,415,707,630,683,222,2,149,59,284,104,416,708,631,684,223,3,150,60,285,105,417,709,632,685,224,4,151,61,286,106,403,710,633,686,225,5,152,62,272,107,404,711,634,687,226,6,153,63,273,108,405,712,621,688,227,7,154,64,274,109,406,699,622,689,214,8,155,65,275,110,407,700,623,690,215,0,156,66,276,111,408,795,784,787,772,762,768,764,277,112,409,731,732,733,734,806,810,807,808,804,805,809,751,752,753,750,847,837,859,865,841,869,835,867,833,836,335,258,213,138,37,392,463,614,302,666,336,667,259,200,139,38,393,464,615,303,337,668,260,201,140,39,394,465,616,304,261,669,338,202,141,40,395,466,617,305,670,262,339,203,142,41,396,467,618,306,671,263,340,204,129,42,397,468,619,307,672,264,341,205,130,29,398,469,620,308,673,265,342,206,131,30,399,470,606,309,674,266,343,207,132,31,400,471,607,310,675,267,344,208,133,32,401,472,608,311,676,268,331,209,134,33,402,473,609,312,663,269,332,210,135,34,389,474,610,313,664,270,333,211,136,35,390,475,611,314,665,271,334,212,137,36,391,476,612,315,786,773,775,771,767,763,777,462,613,301,727,728,729,730,799,800,801,802,803,797,798,747,748,749,746,874,870,872,844,853,849,842,852,856,860,517,525,550,287,126,534,357,245,163,172,518,173,526,551,288,127,535,358,246,164,519,174,527,552,289,128,536,359,247,165,528,175,506,553,290,115,537,345,248,166,176,529,507,554,291,116,538,346,249,167,177,530,508,555,292,117,539,347,250,168,178,531,509,556,293,118,540,348,251,169,179,532,510,557,294,119,541,349,252,170,180,533,511,558,295,120,542,350,253,171,181,520,512,559,296,121,543,351,254,157,182,521,513,560,297,122,544,352,255,158,183,522,514,561,298,123,545,353,256,159,184,523,515,548,299,124,546,354,257,160,185,524,516,549,300,125,547,355,243,161,769,780,779,782,774,766,781,356,244,162,691,692,693,694,793,794,788,789,790,791,792,756,742,743,757,873,875,871,832,862,845,830,838,828,848 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 876 = 1 + 5*175, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#e7b09742a16e6864ff6d25441ad87c147aa31aca9a94ae58d8a86bc95f641fe7, M = {165} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 175): MacNeish's product over GF(25) x GF(7); GF(25) = F_5[x]/(x^2 + 2); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 51.

last edited by qawbecrdtey at 2026-10-06 15:27:42 · history