Equation 677 Database

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Magma 146bf14d8147…

magma 146bf14d8147
Size
705
Isomorphism class hash
146bf14d8147fb45539ca3dc3b1361dc1b38cd39619bfd3e55195b495d466bb0
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 19:51:27
Display reorder
660,545,198,145,85,346,546,196,347,146,86,547,197,348,147,84,201,544,349,144,88,199,542,350,142,89,200,543,351,143,87,352,193,151,536,91,353,194,152,537,92,354,195,153,538,90,192,355,150,539,94,190,356,148,540,95,191,357,149,541,93,669,672,666,671,581,55,204,280,391,582,56,392,202,281,583,54,393,203,282,58,580,390,207,283,59,578,388,205,284,57,579,389,206,285,382,53,210,572,278,383,51,208,573,279,384,52,209,574,277,49,385,213,575,274,50,386,211,576,275,48,387,212,577,276,689,691,687,686,427,487,29,511,463,428,488,464,27,512,429,489,465,28,513,486,426,462,25,510,484,424,460,26,508,485,425,461,24,509,454,478,35,418,502,455,479,33,419,503,456,480,34,420,504,481,457,31,421,505,482,458,32,422,506,483,459,30,423,507,664,667,668,665,159,237,36,533,220,157,235,221,37,534,158,236,222,38,535,233,155,223,39,532,234,156,224,40,530,232,154,225,41,531,218,228,42,165,524,219,226,43,163,525,217,227,44,164,526,231,214,45,161,527,229,215,46,162,528,230,216,47,160,529,673,675,679,677,593,15,238,403,379,594,16,380,239,404,595,17,381,240,405,14,592,378,241,402,12,590,376,242,400,13,591,377,243,401,370,21,244,584,394,371,22,245,585,395,372,23,246,586,396,20,373,247,587,397,18,374,248,588,398,19,375,249,589,399,670,662,663,661,439,557,103,0,367,440,558,368,104,2,441,559,369,102,1,556,438,366,106,4,554,436,364,107,5,555,437,365,105,3,358,548,101,430,7,359,549,99,431,8,360,550,100,432,6,551,361,97,433,10,552,362,98,434,11,553,363,96,435,9,695,698,693,694,120,523,130,651,617,654,653,655,131,652,657,656,658,132,659,522,121,616,133,648,520,122,614,134,649,521,123,615,135,650,608,514,136,124,643,609,515,137,125,644,610,516,138,126,642,517,611,139,127,646,518,612,140,128,647,519,613,141,129,645,701,703,702,704,114,627,253,569,451,115,628,452,254,570,116,629,453,255,571,626,117,450,252,568,624,118,448,250,566,625,119,449,251,567,442,618,259,112,560,443,619,260,113,561,444,620,261,111,562,621,445,258,108,563,622,446,256,109,564,623,447,257,110,565,697,700,699,696,475,499,83,335,185,476,500,186,81,336,477,501,184,82,334,498,474,188,79,338,496,472,189,80,339,497,473,187,78,337,183,490,74,466,341,181,491,72,467,342,182,492,73,468,340,493,179,77,469,344,494,180,75,470,345,495,178,76,471,343,676,678,684,682,639,605,268,415,62,640,606,60,269,416,641,607,61,270,417,604,638,65,271,414,602,636,63,272,412,603,637,64,273,413,68,596,266,630,406,66,597,267,631,407,67,598,265,632,408,599,71,262,633,409,600,69,263,634,410,601,70,264,635,411,683,681,674,680,326,309,166,313,294,327,307,292,167,314,325,308,293,168,315,305,322,297,169,312,306,323,295,170,310,304,324,296,171,311,289,300,172,332,319,290,298,173,333,320,291,299,174,331,321,303,288,175,328,318,301,286,176,329,316,302,287,177,330,317,690,688,692,685 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#b24873ef385d9876d07add1b0ccd1e5b9965acff1b69e8225210d446f480d74b, M = {60} 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, 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 19:51:28 · history