Equation 677 Database

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Magma 6612d50c4945…

magma 6612d50c4945
Size
705
Isomorphism class hash
6612d50c494572f41d2a079d8f144d8e67928350c443bf08358860cc1124aefe
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 20:09:20
Display reorder
660,485,481,24,486,488,501,25,506,505,508,520,26,525,528,526,27,461,466,465,468,28,428,431,430,432,29,441,446,445,448,601,30,606,605,608,620,31,626,625,628,640,32,646,645,648,33,581,586,585,588,34,540,546,545,548,35,561,566,565,568,685,702,689,688,492,493,0,489,495,513,2,509,512,515,533,1,532,535,529,4,473,469,472,475,5,439,437,438,427,3,453,449,452,455,613,7,609,612,615,633,8,629,632,635,653,6,649,652,655,10,593,589,592,597,11,553,549,552,557,9,573,569,572,577,686,693,694,692,407,373,180,301,349,374,178,302,408,350,375,179,409,351,303,183,372,300,406,348,181,370,298,404,346,182,371,299,405,347,379,186,307,413,355,380,184,308,414,356,381,185,309,415,357,189,378,306,412,354,187,376,304,410,352,188,377,305,411,353,675,666,671,680,220,91,272,134,116,92,273,132,221,114,90,271,222,115,133,268,94,137,223,119,269,95,135,224,117,270,93,136,225,118,89,263,140,218,111,87,264,138,219,112,88,262,139,217,113,266,85,143,214,110,267,86,141,215,108,265,84,142,216,109,661,668,677,676,491,494,71,487,490,514,69,507,511,510,534,70,531,530,527,67,474,467,471,470,68,426,423,425,424,66,454,447,451,450,614,62,607,611,610,634,60,627,631,630,654,61,647,651,650,65,594,587,591,590,63,554,547,551,550,64,574,567,571,570,700,691,703,696,498,499,96,497,480,519,97,517,518,500,539,98,537,521,538,99,479,478,477,460,100,422,420,421,429,101,459,458,457,440,619,102,617,618,600,637,103,639,638,621,659,104,658,657,641,105,599,596,595,580,106,559,556,555,541,107,579,576,575,560,697,701,704,699,483,482,14,484,496,502,12,504,503,516,522,13,523,536,524,17,462,464,463,476,15,434,436,435,433,16,442,444,443,456,602,20,604,603,616,622,18,624,623,636,642,19,644,643,656,23,582,584,583,598,21,542,544,543,558,22,562,564,563,578,690,687,695,698,55,83,126,382,337,81,127,383,56,338,82,128,54,339,384,129,79,385,58,336,130,80,386,59,334,131,78,387,57,335,74,124,388,53,343,72,125,417,51,344,73,123,418,52,345,120,77,389,49,342,121,75,390,50,340,122,76,391,48,341,683,682,670,672,230,325,45,243,253,326,46,241,231,254,327,47,229,255,242,44,324,239,226,252,42,322,240,227,250,43,323,238,228,251,331,36,249,236,259,332,37,247,237,260,333,38,248,235,261,39,330,245,232,258,40,328,246,233,256,41,329,244,234,257,669,673,662,684,289,197,166,152,395,198,167,150,290,396,196,168,291,397,151,169,200,155,288,394,170,201,153,286,392,171,199,154,287,393,195,172,147,295,401,193,173,148,296,402,194,174,149,297,403,175,191,146,294,400,176,192,144,292,398,177,190,145,293,399,679,665,678,664,313,277,213,361,161,278,211,362,314,162,279,212,315,160,363,209,276,360,312,164,210,274,358,310,165,208,275,359,311,163,283,204,367,319,159,284,202,368,320,416,285,203,369,321,419,207,282,366,318,158,205,280,364,316,156,206,281,365,317,157,663,674,681,667 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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#bc5f623c03e0cf031de7da5cba3786bb6161d1a009770b59759abcaaa846aef4, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 20:09:21 · history