Equation 677 Database

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Magma f89a21b3c022…

magma f89a21b3c022
Size
870
Isomorphism class hash
f89a21b3c022cf44a3287ca0c80f657a1d50b5f88562bb8a868d3b76c1a1265f
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 869) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 19:56:11
Display reorder
869,189,732,760,717,190,733,761,718,191,734,762,719,192,720,763,705,193,721,764,706,194,722,750,707,180,723,751,708,181,724,752,709,182,725,753,710,183,726,754,711,184,727,755,712,185,728,756,713,186,729,757,714,187,730,758,715,731,188,759,716,743,735,736,737,738,739,740,741,742,745,746,747,748,749,744,837,831,832,834,25,636,614,621,26,637,600,622,27,638,601,623,28,639,602,624,29,640,603,625,15,641,604,626,16,642,605,627,17,643,606,628,18,644,607,629,19,630,608,615,20,631,609,616,21,632,610,617,22,633,611,618,23,634,612,619,635,24,613,620,597,589,590,591,592,593,594,595,596,599,585,586,587,588,598,839,826,825,833,118,315,294,300,119,316,295,301,105,317,296,302,106,318,297,303,107,319,298,304,108,320,299,305,109,321,285,306,110,322,286,307,111,323,287,308,112,324,288,309,113,325,289,310,114,326,290,311,115,327,291,312,116,328,292,313,329,117,293,314,276,283,284,270,271,272,273,274,275,278,279,280,281,282,277,840,843,848,836,570,63,93,48,571,64,94,49,572,65,95,50,573,66,96,51,574,67,97,52,575,68,98,53,576,69,99,54,577,70,100,55,578,71,101,56,579,72,102,57,580,73,103,58,581,74,104,59,582,60,90,45,583,61,91,46,62,584,92,47,76,83,84,85,86,87,88,89,75,78,79,80,81,82,77,842,866,865,841,36,535,564,519,37,536,565,520,38,537,566,521,39,538,567,522,40,539,568,523,41,525,569,524,42,526,555,510,43,527,556,511,44,528,557,512,30,529,558,513,31,530,559,514,32,531,560,515,33,532,561,516,34,533,562,517,534,35,563,518,546,553,554,540,541,542,543,544,545,548,549,550,551,552,547,849,863,862,846,120,495,474,480,121,496,475,481,122,497,476,482,123,498,477,483,124,499,478,484,125,500,479,485,126,501,465,486,127,502,466,487,128,503,467,488,129,504,468,489,130,505,469,490,131,506,470,491,132,507,471,492,133,508,472,493,509,134,473,494,457,464,450,451,452,453,454,455,456,459,460,461,462,463,458,838,859,858,835,201,269,232,254,202,255,233,240,203,256,234,241,204,257,235,242,205,258,236,243,206,259,237,244,207,260,238,245,208,261,239,246,209,262,225,247,195,263,226,248,196,264,227,249,197,265,228,250,198,266,229,251,199,267,230,252,268,200,231,253,214,221,222,223,224,210,211,212,213,216,217,218,219,220,215,855,868,867,856,179,775,804,812,165,776,805,813,166,777,806,814,167,778,807,815,168,779,808,816,169,765,809,817,170,766,795,818,171,767,796,819,172,768,797,820,173,769,798,821,174,770,799,822,175,771,800,823,176,772,801,824,177,773,802,810,774,178,803,811,787,794,780,781,782,783,784,785,786,789,790,791,792,793,788,860,852,851,857,157,693,670,678,158,694,671,679,159,695,672,680,160,696,673,681,161,697,674,682,162,698,660,683,163,699,661,684,164,700,662,685,150,701,663,686,151,702,664,687,152,703,665,688,153,704,666,689,154,690,667,675,155,691,668,676,692,156,669,677,651,658,659,645,646,647,648,649,650,653,654,655,656,657,652,850,854,853,844,145,403,433,439,146,404,434,440,147,390,420,441,148,391,421,442,149,392,422,443,135,393,423,444,136,394,424,445,137,395,425,446,138,396,426,447,139,397,427,448,140,398,428,449,141,399,429,435,142,400,430,436,143,401,431,437,402,144,432,438,414,406,407,408,409,410,411,412,413,416,417,418,419,405,415,830,829,828,827,5,357,385,341,6,358,386,342,7,359,387,343,8,345,388,344,9,346,389,330,10,347,375,331,11,348,376,332,12,349,377,333,13,350,378,334,14,351,379,335,1,352,380,336,0,353,381,337,2,354,382,338,3,355,383,339,356,4,384,340,368,360,361,362,363,364,365,366,367,370,371,372,373,374,369,864,847,845,861 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 870 = 1 + 11*79, 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, 11, B) with E = magma#5e76c6d3b965544f3246a1396d58a622a92ac5abe1044f6db52aefba39d6a87c, M = {75} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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(11, 79): MacNeish's product over GF(79); 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: 45.

last edited by qawbecrdtey at 2026-10-07 19:56:12 · history