Equation 677 Database

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Magma 7ee54238f365…

magma 7ee54238f365
Size
705
Isomorphism class hash
7ee54238f365536cbe238251cb7ff99d9765aa7ca3178bbb30434b8ca74c84bc
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 19:15:02
Display reorder
660,308,288,222,444,224,309,286,220,442,225,307,287,221,443,223,284,311,218,440,227,285,312,219,441,228,283,310,217,439,226,213,294,314,450,230,211,292,315,448,231,212,293,313,449,229,290,216,317,446,233,291,214,318,447,234,289,215,316,445,232,663,672,668,661,61,177,571,163,501,62,175,569,164,499,60,176,570,165,500,180,64,567,166,497,178,65,568,167,498,179,63,566,168,496,577,183,67,169,507,575,181,68,170,505,576,182,66,171,506,186,573,70,172,503,184,574,71,173,504,185,572,69,174,502,691,688,690,685,138,513,250,47,456,136,511,251,45,454,137,512,252,46,455,509,134,249,43,452,510,135,247,44,453,508,133,248,42,451,256,519,129,38,462,257,517,127,36,460,258,518,128,37,461,515,255,132,41,458,516,253,130,39,459,514,254,131,40,457,669,664,662,666,99,468,119,194,558,100,466,117,195,556,101,467,118,193,557,464,98,122,197,561,465,96,120,198,559,463,97,121,196,560,593,474,105,192,592,123,472,106,190,562,590,473,107,191,591,470,126,104,188,565,471,124,102,189,563,469,125,103,187,564,677,681,680,676,365,629,489,537,206,366,627,487,535,207,364,628,488,536,205,625,361,485,533,209,626,362,486,534,210,624,363,484,532,208,495,635,356,543,204,493,633,357,541,202,494,634,355,542,203,631,491,359,539,200,632,492,360,540,201,630,490,358,538,199,667,670,665,671,240,348,396,341,327,238,346,394,342,325,239,347,395,340,326,344,236,392,337,330,345,237,393,338,328,343,235,391,339,329,402,354,246,332,322,400,352,244,333,323,401,353,245,331,324,350,398,242,335,321,351,399,243,336,319,349,397,241,334,320,698,697,696,694,6,116,619,480,599,7,114,620,478,597,8,115,618,479,598,112,9,615,476,595,113,10,616,477,596,111,11,617,475,594,659,657,4,656,658,651,649,5,648,650,655,653,3,652,654,110,621,1,482,601,108,622,0,483,602,109,623,2,481,600,702,703,704,701,82,140,608,384,377,83,141,606,382,378,81,139,607,383,376,143,78,604,380,373,144,79,605,381,374,142,80,603,379,375,614,146,73,390,368,612,147,74,388,369,613,145,72,389,367,149,610,76,386,371,150,611,77,387,372,148,609,75,385,370,695,700,699,693,305,12,583,278,432,306,13,581,279,430,304,14,582,277,431,15,301,579,281,428,16,302,580,282,429,17,303,578,280,427,589,18,296,276,438,587,19,297,274,436,588,20,295,275,437,21,585,299,272,434,22,586,300,273,435,23,584,298,271,433,673,675,679,684,158,408,549,84,641,159,406,547,85,639,157,407,548,86,640,404,161,545,87,637,405,162,546,88,638,403,160,544,89,636,555,414,156,90,647,553,412,154,91,645,554,413,155,92,646,410,551,152,93,643,411,552,153,94,644,409,550,151,95,642,682,683,678,674,423,26,525,54,259,421,24,523,55,260,422,25,524,56,261,29,426,521,57,262,27,424,522,58,263,28,425,520,59,264,531,32,418,52,265,529,30,419,53,266,530,31,420,51,267,35,527,417,48,268,33,528,415,49,269,34,526,416,50,270,686,687,689,692 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#9613877152071542ba1176ebd2d9075b5c9b63b690264e2f5c72257d6a275b00, 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 19:15:03 · history