Equation 677 Database

← all  ·  ← by size  ·  ← size 870

Magma 062b5e060dda…

magma 062b5e060dda
Size
870
Isomorphism class hash
062b5e060ddad84f7d98c0432fc11c70dfc6bf04975da47f404a71c4e67c3150
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
2026-10-08 01:21:58
Display reorder
869,169,772,798,810,170,773,799,811,171,774,800,812,172,775,801,813,173,776,802,814,174,777,803,815,175,778,804,816,176,779,805,817,177,765,806,818,178,766,807,819,179,767,808,820,768,165,809,821,769,166,795,822,770,167,796,823,771,168,797,824,781,788,789,790,791,792,793,794,780,783,784,785,786,787,782,840,825,826,835,122,732,759,718,123,733,760,719,124,734,761,705,125,720,762,706,126,721,763,707,127,722,764,708,128,723,750,709,129,724,751,710,130,725,752,711,131,726,753,712,132,727,754,713,728,133,755,714,729,134,756,715,730,120,757,716,731,121,758,717,741,748,749,735,736,737,738,739,740,743,744,745,746,747,742,853,839,845,849,108,647,686,698,109,648,687,699,110,649,688,700,111,650,689,701,112,651,675,702,113,652,676,703,114,653,677,704,115,654,678,690,116,655,679,691,117,656,680,692,118,657,681,693,658,119,682,694,659,105,683,695,645,106,684,696,646,107,685,697,669,661,662,663,664,665,666,667,668,671,672,673,674,660,670,841,827,832,836,314,511,550,561,300,512,551,562,301,513,552,563,302,514,553,564,303,515,554,565,304,516,540,566,305,517,541,567,306,518,542,568,307,519,543,569,308,520,544,555,309,521,545,556,522,310,546,557,523,311,547,558,524,312,548,559,510,313,549,560,533,525,526,527,528,529,530,531,532,535,536,537,538,539,534,843,828,834,844,13,427,399,412,14,428,400,413,1,429,401,414,0,430,402,415,2,431,403,416,3,432,404,417,4,433,390,418,5,434,391,419,6,420,392,405,7,421,393,406,8,422,394,407,423,9,395,408,424,10,396,409,425,11,397,410,426,12,398,411,382,389,375,376,377,378,379,380,381,384,385,386,387,388,383,833,864,866,831,505,282,254,266,506,283,240,267,507,284,241,268,508,270,242,269,509,271,243,255,495,272,244,256,496,273,245,257,497,274,246,258,498,275,247,259,499,276,248,260,500,277,249,261,278,501,250,262,279,502,251,263,280,503,252,264,281,504,253,265,289,296,297,298,299,285,286,287,288,291,292,293,294,295,290,829,842,847,830,640,187,214,226,641,188,215,227,642,189,216,228,643,190,217,229,644,191,218,230,630,192,219,231,631,193,220,232,632,194,221,233,633,180,222,234,634,181,223,235,635,182,224,236,183,636,210,237,184,637,211,238,185,638,212,239,186,639,213,225,196,203,204,205,206,207,208,209,195,198,199,200,201,202,197,865,851,859,863,95,361,335,346,96,362,336,347,97,363,337,348,98,364,338,349,99,365,339,350,100,366,340,351,101,367,341,352,102,368,342,353,103,369,343,354,104,370,344,355,90,371,330,356,372,91,331,357,373,92,332,358,374,93,333,359,360,94,334,345,317,324,325,326,327,328,329,315,316,319,320,321,322,323,318,854,837,846,857,22,57,83,43,23,58,84,44,24,59,85,30,25,45,86,31,26,46,87,32,27,47,88,33,28,48,89,34,29,49,75,35,15,50,76,36,16,51,77,37,17,52,78,38,53,18,79,39,54,19,80,40,55,20,81,41,56,21,82,42,64,71,72,73,74,60,61,62,63,66,67,68,69,70,65,861,868,867,862,143,600,574,586,144,601,575,587,145,602,576,588,146,603,577,589,147,604,578,590,148,605,579,591,149,606,580,592,135,607,581,593,136,608,582,594,137,609,583,595,138,610,584,596,611,139,570,597,612,140,571,598,613,141,572,599,614,142,573,585,622,629,615,616,617,618,619,620,621,624,625,626,627,628,623,852,850,860,858,154,462,487,446,155,463,488,447,156,464,489,448,157,450,490,449,158,451,491,435,159,452,492,436,160,453,493,437,161,454,494,438,162,455,480,439,163,456,481,440,164,457,482,441,458,150,483,442,459,151,484,443,460,152,485,444,461,153,486,445,470,477,478,479,465,466,467,468,469,472,473,474,475,476,471,855,838,848,856 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#7c9587bb487c7f78877b32bd3c6516b6b04394ef6d405ed5492c6ed5480f025c, M = {75} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 2026-10-08 01:21:59 · history