Equation 677 Database

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Magma 843612279232…

magma 843612279232
Size
705
Isomorphism class hash
8436122792328d11cb219f1713c77ead88c879d4c5915ced07346d0161a8fdfb
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 19:54:34
Display reorder
660,275,231,286,471,507,273,232,508,287,472,274,233,509,285,473,230,271,506,282,470,228,272,504,283,468,229,270,505,284,469,237,266,513,277,477,238,264,514,278,478,239,265,515,276,479,269,236,512,280,476,281,267,234,510,474,268,235,511,279,475,679,680,677,682,73,188,330,387,59,74,186,57,331,388,72,187,58,332,389,191,76,55,333,386,189,77,56,334,384,190,75,54,335,385,183,79,50,328,393,184,80,48,329,394,185,78,49,327,395,82,182,53,324,392,325,83,180,51,390,81,181,52,326,391,668,670,663,661,375,203,347,370,359,376,201,357,345,371,377,202,358,346,369,199,374,355,343,366,200,372,356,344,367,198,373,354,342,368,194,381,350,338,361,192,382,348,336,362,193,383,349,337,360,380,197,353,341,364,339,378,195,351,365,379,196,352,340,363,675,683,673,674,89,298,539,164,519,90,299,520,540,165,88,297,521,541,166,294,85,518,538,163,295,86,516,536,161,296,87,517,537,162,289,636,639,640,638,290,645,647,648,646,288,653,655,656,654,629,292,630,633,632,542,135,293,522,167,84,291,523,543,160,703,697,704,699,257,70,555,241,495,255,71,496,556,242,256,69,497,557,240,66,253,494,554,244,67,254,492,552,245,68,252,493,553,243,61,263,501,561,247,62,261,502,562,248,60,262,503,563,246,259,64,500,560,250,558,260,65,498,251,258,63,499,559,249,689,692,691,693,399,114,149,527,447,400,112,448,150,528,401,113,449,148,529,110,398,446,152,526,111,396,444,153,524,109,397,445,151,525,105,405,453,155,533,103,406,454,156,534,104,407,455,154,535,404,108,452,158,532,159,402,106,450,530,403,107,451,157,531,664,665,669,672,419,316,430,115,435,417,317,436,431,116,418,315,437,429,117,312,415,434,426,118,313,416,432,427,119,314,414,433,428,120,322,410,441,421,121,323,408,442,422,122,321,409,443,420,123,413,318,440,424,124,425,411,319,438,125,412,320,439,423,126,695,690,696,694,599,102,44,222,619,600,100,620,42,223,601,101,621,43,224,98,598,618,47,225,99,596,616,45,226,97,597,617,46,227,93,605,625,39,220,91,606,626,40,221,92,607,627,41,219,604,96,624,38,216,36,602,94,622,217,603,95,623,37,218,686,688,681,676,591,211,611,129,548,592,212,549,612,127,593,210,550,613,128,214,590,547,610,132,215,588,545,608,130,213,589,546,609,131,209,642,641,643,637,207,650,649,651,644,208,658,657,659,652,635,205,634,631,628,614,594,206,551,133,595,204,544,615,134,701,700,698,702,147,179,459,567,1,145,177,0,460,568,146,178,2,461,569,175,143,3,458,566,176,144,4,456,564,174,142,5,457,565,170,138,6,465,573,168,136,7,466,574,169,137,8,467,575,141,173,9,464,572,462,139,171,10,570,140,172,11,463,571,667,662,671,666,13,311,28,483,579,14,309,580,29,484,12,310,581,27,485,307,16,578,24,482,308,17,576,25,480,306,15,577,26,481,302,19,585,34,489,300,20,586,35,490,301,18,587,33,491,22,305,584,30,488,31,23,303,582,486,21,304,583,32,487,687,684,678,685 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#b356224f433e80b1c4ac338e7aaea2066ee34f4a7233e2d09dbcc6e7070accf0, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 19:54:35 · history