Equation 677 Database

← all  ·  ← by size  ·  ← size 941

Magma a062d7f589a8…

magma a062d7f589a8
Size
941
Isomorphism class hash
a062d7f589a8966b7e7d0d5eb0b0e02d3389c235bd768c2ea42c2f163640581d
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 940) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 14:18:02
Display reorder
940,32,62,46,816,456,341,722,587,472,331,706,597,581,450,325,728,603,466,347,712,33,63,47,817,457,342,723,588,473,332,707,598,582,451,326,729,604,467,348,713,34,56,40,818,458,343,724,589,474,333,708,599,583,452,327,730,605,468,349,714,35,57,41,819,459,336,725,590,475,334,709,592,576,453,320,731,606,469,350,715,36,58,42,812,460,337,726,591,476,335,710,593,577,454,321,732,607,470,351,716,37,59,43,813,461,338,727,584,477,328,711,594,717,578,455,322,733,600,471,344,38,60,44,814,462,339,720,585,478,329,704,595,718,579,448,323,734,601,464,345,39,61,45,815,463,340,721,586,479,330,705,596,719,580,449,324,735,602,465,346,55,48,49,51,52,53,54,50,846,844,845,912,890,867,923,917,893,876,895,932,894,875,925,938,913,889,930,843,760,744,754,830,562,292,420,99,552,308,442,121,105,568,314,426,115,546,298,436,761,745,755,800,563,293,421,100,553,309,443,122,106,569,315,427,116,547,299,437,762,746,756,802,564,294,422,101,554,310,444,123,107,570,316,428,117,548,300,438,763,747,757,820,565,295,423,102,555,311,445,124,108,571,317,429,118,549,301,439,764,748,758,823,566,288,416,103,556,304,446,125,109,572,318,430,119,550,302,432,765,749,759,825,567,289,417,96,557,305,447,126,433,110,573,319,431,112,551,303,766,750,752,827,560,290,418,97,558,306,440,127,434,111,574,312,424,113,544,296,767,751,753,829,561,291,419,98,559,307,441,120,435,104,575,313,425,114,545,297,737,738,739,741,742,743,736,740,927,896,926,866,851,864,903,934,874,882,873,881,916,920,872,850,929,849,865,928,235,245,229,805,626,370,497,684,616,360,481,702,678,632,354,511,691,610,376,495,236,246,230,806,627,371,498,685,617,361,482,703,679,633,355,504,694,611,377,488,237,247,231,807,628,372,499,686,618,362,483,696,672,634,356,505,695,612,378,489,238,240,224,808,629,373,500,687,619,363,484,697,673,635,357,506,692,613,379,490,239,241,225,809,630,374,501,680,620,364,485,698,674,636,358,507,693,614,380,491,232,242,226,810,631,375,502,681,621,365,486,699,492,675,637,359,508,688,615,381,233,243,227,811,624,368,503,682,622,366,487,700,493,676,638,352,509,689,608,382,234,244,228,804,625,369,496,683,623,367,480,701,494,677,639,353,510,690,609,383,250,251,252,254,255,248,249,253,860,909,910,914,892,869,891,883,918,885,933,884,877,886,878,935,931,924,868,859,771,795,781,837,200,138,17,77,216,154,0,87,71,194,148,31,93,210,132,15,772,796,782,838,201,139,18,78,217,155,2,80,64,195,149,24,94,211,133,8,773,797,783,839,202,140,19,79,218,156,3,81,65,196,150,25,95,212,134,9,774,798,776,832,203,141,20,72,219,157,4,82,66,197,151,26,88,213,135,10,775,799,777,833,204,142,21,73,220,158,5,83,67,198,144,27,89,214,128,11,768,792,778,834,205,143,22,74,221,159,6,84,12,68,199,145,28,90,215,129,769,793,779,835,206,136,23,75,222,152,7,85,13,69,192,146,29,91,208,130,770,794,780,836,207,137,16,76,223,153,1,86,14,70,193,147,30,92,209,131,787,788,789,791,784,785,786,790,899,897,939,904,848,853,847,907,842,906,900,908,841,858,840,902,852,901,854,898,408,392,402,801,516,276,191,644,532,266,175,666,650,522,260,177,660,538,282,161,409,393,403,821,517,277,184,645,533,267,168,667,651,523,261,178,661,539,283,162,410,394,404,822,518,278,185,646,534,268,169,668,652,524,262,179,662,540,284,163,411,395,405,824,519,279,186,647,535,269,170,669,653,525,263,180,663,541,285,164,412,396,406,826,512,272,187,640,528,270,171,670,654,526,256,181,656,542,286,165,413,397,407,828,513,273,188,641,529,271,172,671,166,655,527,257,182,657,543,287,414,398,400,831,514,274,189,642,530,264,173,664,167,648,520,258,183,658,536,280,415,399,401,803,515,275,190,643,531,265,174,665,160,649,521,259,176,659,537,281,385,386,387,389,390,391,384,388,870,871,936,911,888,862,921,880,856,937,905,879,855,919,857,922,863,887,861,915 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 941 = 1 + 5*188, 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#892b5616c7779dfec415627d945de6de06210babab60b9ffd32cbcc3e1be41da, M = {168} 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, 188): MacNeish's product over GF(4) x GF(47); GF(4) = F_2[x]/(x^2 + x + 1); 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: 101.

last edited by qawbecrdtey at 2026-10-07 14:18:03 · history