Equation 677 Database

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Magma 958eba84ed7d…

magma 958eba84ed7d
Size
876
Isomorphism class hash
958eba84ed7d47c620dd80b0429995286a1dd127e2a85d4bd2b64745689d5e6d
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 826 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 00:58:38
Display reorder
857,279,405,7,702,242,267,393,9,690,244,268,394,10,691,245,269,395,11,692,246,270,396,12,693,247,271,397,13,694,248,398,272,0,695,249,399,273,1,696,250,400,274,2,697,251,401,275,3,698,252,276,402,4,699,239,277,403,5,700,240,241,404,278,6,701,280,406,8,689,243,561,357,451,133,601,548,358,452,134,602,549,359,453,135,603,550,360,454,136,604,551,361,455,137,590,552,362,456,138,591,553,363,457,139,592,554,364,458,140,593,555,351,459,126,594,556,352,460,127,595,557,353,461,128,596,558,354,462,129,597,559,355,463,130,598,560,356,449,131,599,802,807,791,817,800,814,804,450,132,600,706,703,704,705,819,820,821,822,823,824,818,713,722,718,714,867,848,852,842,855,853,844,850,854,847,347,184,332,32,65,349,186,334,34,67,350,187,335,35,68,337,188,336,36,69,338,189,323,37,56,339,190,324,38,57,191,340,325,39,58,192,341,326,40,59,193,342,327,41,60,194,343,328,28,61,344,195,329,29,62,345,196,330,30,63,64,183,346,331,31,348,185,333,33,66,95,200,180,233,486,96,201,181,234,487,97,202,182,235,488,84,203,169,236,489,85,204,170,237,490,86,205,171,238,491,87,206,172,225,478,88,207,173,226,479,89,208,174,227,480,90,209,175,228,481,91,210,176,229,482,92,197,177,230,483,93,198,178,231,484,94,199,179,232,485,757,751,756,743,744,746,752,798,799,808,793,794,795,796,742,737,738,739,740,782,741,710,721,717,709,870,843,875,856,830,839,841,840,828,838,444,83,538,577,125,446,71,540,579,113,447,72,541,580,114,448,73,542,581,115,435,74,543,582,116,436,75,544,583,117,76,437,545,584,118,77,438,546,585,119,78,439,547,586,120,79,440,534,587,121,441,80,535,588,122,442,81,536,589,123,124,82,443,537,576,445,70,539,578,112,640,288,258,383,686,641,289,259,384,687,642,290,260,385,688,643,291,261,386,675,644,292,262,387,676,645,293,263,388,677,646,294,264,389,678,633,281,265,390,679,634,282,266,391,680,635,283,253,392,681,636,284,254,379,682,637,285,255,380,683,638,286,256,381,684,639,287,257,382,685,760,745,773,775,748,778,754,801,806,816,809,810,811,812,770,762,763,764,765,766,767,712,768,769,711,862,871,872,836,829,827,835,825,826,837,308,671,155,424,213,296,673,157,426,215,297,674,158,427,216,298,661,159,428,217,299,662,160,429,218,300,663,161,430,219,664,301,162,431,220,665,302,163,432,221,666,303,164,433,222,667,304,165,434,223,305,668,166,421,224,306,669,167,422,211,212,670,307,168,423,295,672,156,425,214,629,105,520,311,377,630,106,521,312,378,631,107,522,313,365,632,108,523,314,366,619,109,524,315,367,620,110,525,316,368,621,111,526,317,369,622,98,527,318,370,623,99,528,319,371,624,100,529,320,372,625,101,530,321,373,626,102,531,322,374,627,103,532,309,375,628,104,533,310,376,755,779,750,759,753,777,747,813,803,805,783,788,789,790,735,736,728,727,723,780,724,725,720,716,726,874,873,859,860,858,863,864,861,868,865,505,519,575,477,617,493,507,563,465,605,494,508,564,466,606,495,509,565,467,607,496,510,566,468,608,497,511,567,469,609,512,498,568,470,610,513,499,569,471,611,514,500,570,472,612,515,501,571,473,613,502,516,572,474,614,503,517,573,475,615,616,518,504,574,476,492,506,562,464,618,152,414,47,648,26,153,415,48,649,27,154,416,49,650,14,141,417,50,651,15,142,418,51,652,16,143,419,52,653,17,144,420,53,654,18,145,407,54,655,19,146,408,55,656,20,147,409,42,657,21,148,410,43,658,22,149,411,44,659,23,150,412,45,660,24,151,413,46,647,25,771,772,774,761,776,749,758,797,815,792,784,785,786,787,729,730,731,732,733,781,734,708,719,715,707,866,869,851,834,845,849,846,833,832,831 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#99cb45b67a2dc9ee437518638e58d067aa46b7acbabf3a3a9e16b3d48cee22eb, 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 2026-10-07 00:58:39 · history