Equation 677 Database

← all  ·  ← by size  ·  ← size 945

Magma a5561d779e08…

magma a5561d779e08
Size
945
Isomorphism class hash
a5561d779e08de20ac12fbbe0d4e0941f569fb5c6998b7c9ce2aa3d0ac80e8d3
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 944) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 16:58:44
Display reorder
85,54,63,74,76,86,55,64,75,77,87,56,65,68,78,88,57,66,69,79,89,58,67,70,80,90,59,60,71,81,91,52,61,72,82,84,53,62,73,83,943,944,941,940,942,559,548,557,556,558,645,621,561,623,638,629,609,634,625,570,528,547,539,538,549,679,677,676,678,661,622,560,624,639,630,610,635,626,571,611,636,628,627,643,637,554,553,555,502,537,0,384,456,403,303,433,385,95,317,447,402,395,483,455,481,480,482,30,378,1,379,457,404,304,434,386,96,318,448,397,396,487,451,485,484,486,31,374,2,380,458,405,305,435,387,97,319,449,398,391,491,452,489,488,392,490,32,375,3,381,459,406,306,436,388,92,320,450,399,495,453,493,492,393,494,33,376,4,382,460,407,307,437,389,93,321,445,400,499,454,497,496,394,498,34,377,5,383,461,408,308,438,390,94,322,446,401,313,314,315,309,310,311,312,316,911,914,912,913,910,885,883,884,882,880,888,881,887,886,889,935,939,936,938,937,350,368,422,416,367,360,341,112,330,123,25,106,324,349,131,334,410,35,103,369,351,423,417,362,361,342,113,331,124,26,107,325,345,132,335,411,36,98,352,370,424,418,363,356,343,574,613,575,565,572,612,618,576,615,631,503,504,531,535,541,633,620,619,617,573,614,648,644,647,658,659,577,616,632,566,505,532,536,542,540,534,533,530,506,529,664,660,663,674,675,127,336,412,37,99,353,371,425,419,100,364,357,344,109,332,125,28,108,326,346,128,337,413,38,354,372,426,420,101,365,358,339,110,328,126,29,104,327,347,129,338,414,39,355,373,421,415,102,366,359,340,111,329,122,27,105,323,348,130,333,409,40,119,120,121,115,116,117,118,114,907,906,909,908,894,896,897,901,903,899,905,900,904,898,902,875,879,876,877,878,563,579,586,589,567,583,590,584,591,581,512,543,510,513,552,642,578,587,562,580,564,650,651,646,649,652,585,592,582,588,544,509,514,551,550,507,511,500,501,508,666,667,662,665,668,158,196,144,181,429,166,204,478,470,136,173,15,20,139,165,188,45,151,189,159,197,145,182,430,167,205,479,471,137,174,14,21,140,161,184,41,152,190,160,198,146,183,431,168,200,477,472,138,175,19,22,141,162,185,17,42,153,191,155,199,147,178,432,169,201,475,473,133,176,23,142,163,186,18,43,154,192,156,194,148,179,427,170,202,476,468,134,177,24,143,164,187,16,44,150,193,157,195,149,180,428,171,203,474,469,135,172,12,13,6,8,9,10,11,7,872,873,871,870,874,928,927,929,926,932,924,931,921,930,923,934,922,933,925,920,216,443,238,260,276,268,219,298,226,262,254,296,244,209,467,50,232,246,289,444,211,239,261,277,269,220,299,227,263,255,297,240,210,462,51,233,247,290,212,439,234,256,278,270,221,607,595,603,601,606,599,593,640,568,598,521,525,515,545,519,602,605,604,594,608,596,656,655,657,654,653,641,569,597,600,526,516,546,520,522,524,523,517,527,518,672,671,673,670,669,463,46,228,248,291,213,440,235,257,292,273,271,222,300,223,264,251,293,241,206,464,47,229,249,214,441,236,258,287,274,272,217,301,224,265,252,294,242,207,465,48,230,250,215,442,237,259,288,275,267,218,302,225,266,253,295,243,208,466,49,231,245,285,286,279,281,282,283,284,280,891,890,895,892,893,863,864,862,860,861,868,867,865,869,866,916,919,915,918,917,820,724,758,784,685,703,795,748,806,734,781,737,767,809,704,831,713,770,839,725,821,759,785,686,696,796,749,807,735,782,738,760,810,705,824,714,771,838,822,726,752,786,687,697,797,750,800,728,783,739,761,811,706,825,715,772,835,823,727,753,787,681,698,798,751,801,729,776,740,762,812,707,826,716,773,836,816,720,754,788,680,699,799,744,802,730,777,741,763,813,708,827,717,774,837,817,721,755,789,834,682,700,792,745,803,731,778,742,764,814,709,828,718,775,818,722,756,790,832,683,701,793,746,804,732,779,743,765,815,710,829,719,768,819,723,757,791,833,684,702,794,747,805,733,780,736,766,808,711,830,712,769,693,694,695,689,690,691,692,688,843,847,849,845,852,840,854,842,841,846,853,848,844,850,851,858,855,857,859,856 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 945 = 45 + 5*180, 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#7d8d7705206e9efc7db192ff528eee0c69daf2633f108d6a813cd9992a6ddd95, M = the submagma generated by {5, 9} (45 elements) 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, 180): MacNeish's product over GF(4) x GF(9) x GF(5); GF(4) = F_2[x]/(x^2 + x + 1), GF(9) = F_3[x]/(x^2 + 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: 105.

last edited by qawbecrdtey at 2026-10-06 16:58:44 · history