Equation 677 Database

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Magma 4a67afb66258…

magma 4a67afb66258
Size
705
Isomorphism class hash
4a67afb662581900886cb0f1570a92c17729c51773d47db0629f1e96395ed6c3
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 17:36:30
Display reorder
660,233,220,483,135,363,234,136,218,484,364,235,134,219,482,362,232,223,486,138,366,230,221,487,139,367,231,222,485,137,365,224,215,481,141,361,225,216,479,142,359,226,217,480,140,360,214,227,477,144,357,212,228,478,145,358,213,229,476,143,356,672,667,661,668,258,100,304,459,623,259,460,98,302,624,257,458,99,303,622,254,103,307,462,626,255,101,305,463,627,256,102,306,461,625,249,106,299,457,621,250,104,300,455,619,248,105,301,456,620,109,252,298,453,617,107,253,296,454,618,108,251,297,452,616,690,685,689,686,205,399,495,519,411,203,520,400,496,412,204,518,398,494,410,201,402,498,522,414,202,403,499,523,415,200,401,497,521,413,211,397,493,517,409,209,395,491,515,407,210,396,492,516,408,393,207,489,513,405,394,208,490,514,406,392,206,488,512,404,663,669,664,671,269,447,387,10,319,270,11,448,388,317,271,9,446,386,318,268,450,390,6,315,266,451,391,7,316,267,449,389,8,314,260,445,385,16,310,261,443,383,17,308,262,444,384,15,309,441,263,381,12,313,442,264,382,13,311,440,265,380,14,312,676,675,673,678,151,507,435,97,423,149,95,508,436,424,150,96,506,434,422,147,510,438,93,426,148,511,439,94,427,146,509,437,92,425,157,505,433,88,421,155,503,431,86,419,156,504,432,87,420,501,153,429,91,417,502,154,430,89,418,500,152,428,90,416,670,666,665,662,123,551,575,21,236,124,22,552,576,237,122,23,550,574,238,126,554,578,20,239,127,555,579,18,240,125,553,577,19,241,129,549,573,27,242,130,547,571,28,243,128,548,572,29,244,545,132,569,26,245,546,133,570,24,246,544,131,568,25,247,696,697,695,694,35,192,177,635,179,33,647,646,644,645,34,634,199,176,178,31,654,652,655,653,32,658,656,659,657,30,650,649,651,648,41,198,171,633,4,39,196,172,631,5,40,197,170,632,3,194,37,174,629,1,195,38,175,630,0,193,36,173,628,2,702,703,701,704,76,73,536,599,159,74,600,636,637,160,75,598,72,543,158,79,641,640,602,162,77,643,642,603,163,78,639,638,601,161,82,71,542,597,165,80,69,540,595,166,81,70,541,596,164,67,85,538,593,168,68,83,539,594,169,66,84,537,592,167,699,700,693,698,353,118,375,587,563,354,588,116,376,564,355,586,117,374,562,352,121,378,590,566,350,119,379,591,567,351,120,377,589,565,344,113,373,585,561,345,114,371,583,559,346,115,372,584,560,112,347,369,581,557,110,348,370,582,558,111,349,368,580,556,679,674,684,681,289,611,531,59,471,287,57,612,532,472,288,58,610,530,470,285,614,534,55,474,286,615,535,56,475,284,613,533,54,473,295,609,529,65,469,293,607,527,63,467,294,608,528,64,468,605,291,525,61,465,606,292,526,62,466,604,290,524,60,464,682,680,677,683,47,187,326,279,336,45,280,188,327,337,46,278,186,328,335,43,190,329,282,332,44,191,330,283,333,42,189,331,281,334,53,185,324,277,342,51,183,325,275,343,52,184,323,276,341,181,49,320,273,338,182,50,321,274,339,180,48,322,272,340,687,688,692,691 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#5a6f57af4478d367dfac6487e89f811f842218c665866e576bd9224bcbc8a047, 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 17:36:31 · history