Equation 677 Database

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Magma cc72732cd1b2…

magma cc72732cd1b2
Size
903
Isomorphism class hash
cc72732cd1b2c28340cfae9e21b2d9a4ea21613446b1bd3289f0ad5c5b8369de
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 902) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 21:31:38
Display reorder
121,122,123,124,125,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,902,0,83,324,2,42,325,3,43,326,4,44,327,5,45,328,6,46,329,7,47,330,8,48,331,9,49,332,10,50,333,11,51,334,12,52,335,13,53,294,14,54,295,15,55,296,16,56,297,17,57,298,18,58,299,19,59,300,20,60,301,21,61,302,22,62,303,23,63,304,24,64,305,25,65,306,26,66,307,27,67,308,28,68,309,29,69,310,30,70,311,31,71,312,32,72,313,33,73,314,34,74,315,35,75,316,36,76,317,37,77,318,38,78,319,320,39,79,40,321,80,41,322,81,323,1,82,363,362,361,360,365,366,367,368,369,370,371,372,373,374,375,376,377,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,364,893,889,887,901,235,273,159,236,274,160,237,275,161,238,276,162,239,277,163,240,278,164,241,279,165,242,280,166,243,281,167,244,282,126,245,283,127,246,284,128,247,285,129,248,286,130,249,287,131,250,288,132,251,289,133,210,290,134,211,291,135,212,292,136,213,293,137,214,252,138,215,253,139,216,254,140,217,255,141,218,256,142,219,257,143,220,258,144,221,259,145,222,260,146,223,261,147,224,262,148,225,263,149,226,264,150,227,265,151,228,266,152,229,267,153,230,268,154,155,231,269,232,156,270,233,157,271,158,234,272,198,197,196,195,200,201,202,203,204,205,206,207,208,209,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,199,888,899,900,886,434,472,510,435,473,511,436,474,512,437,475,513,438,476,514,439,477,515,440,478,516,441,479,517,442,480,518,443,481,519,444,482,520,445,483,521,446,484,522,447,485,523,448,486,524,449,487,525,450,488,526,451,489,527,452,490,528,453,491,529,454,492,530,455,493,531,456,494,532,457,495,533,458,496,534,459,497,535,460,498,536,461,499,537,420,500,538,421,501,539,422,502,540,423,503,541,424,462,542,425,463,543,426,464,544,427,465,545,428,466,504,429,467,505,506,430,468,431,507,469,432,508,470,509,433,471,397,396,395,394,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,398,892,890,894,891,587,625,663,546,626,664,547,627,665,548,628,666,549,629,667,550,588,668,551,589,669,552,590,670,553,591,671,554,592,630,555,593,631,556,594,632,557,595,633,558,596,634,559,597,635,560,598,636,561,599,637,562,600,638,563,601,639,564,602,640,565,603,641,566,604,642,567,605,643,568,606,644,569,607,645,570,608,646,571,609,647,572,610,648,573,611,649,574,612,650,575,613,651,576,614,652,577,615,653,578,616,654,579,617,655,580,618,656,581,619,657,582,620,658,659,583,621,584,660,622,585,661,623,662,586,624,702,701,700,699,704,705,706,707,708,709,710,711,712,713,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,703,896,897,895,898,830,868,752,831,869,753,832,870,754,833,871,755,834,872,714,835,873,715,836,874,716,837,875,717,838,876,718,839,877,719,798,878,720,799,879,721,800,880,722,801,881,723,802,840,724,803,841,725,804,842,726,805,843,727,806,844,728,807,845,729,808,846,730,809,847,731,810,848,732,811,849,733,812,850,734,813,851,735,814,852,736,815,853,737,816,854,738,817,855,739,818,856,740,819,857,741,820,858,742,821,859,743,822,860,744,823,861,745,824,862,746,825,863,747,748,826,864,827,749,865,828,750,866,751,829,867,791,790,789,788,793,794,795,796,797,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,792,883,884,882,885 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 903 = 43 + 5*172, 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#8d34e963a1cc1092729140161eb5f4eda728015af4c47de0cff1dc84270d6c96, M = the submagma generated by {0} (43 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, 172): MacNeish's product over GF(4) x GF(43); 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: 21.

last edited by qawbecrdtey at 2026-10-08 21:31:39 · history