Equation 677 Database

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Magma 2547b8621101…

magma 2547b8621101
Size
705
Isomorphism class hash
2547b8621101960037b8615f8b4dac77b31c870f7908dc46c284a08f81ca1130
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 21:47:08
Display reorder
660,67,476,164,102,440,68,474,162,103,438,66,475,163,104,439,479,63,160,101,443,477,161,99,441,64,478,65,159,100,442,58,155,482,93,446,59,153,480,94,444,57,154,481,95,445,158,61,485,96,449,97,156,62,483,447,157,60,484,98,448,672,663,662,665,107,234,249,368,360,105,235,250,366,361,106,236,251,367,362,237,110,248,371,363,238,246,369,364,108,239,109,247,370,365,113,255,240,374,358,111,256,241,372,359,112,257,242,373,357,254,116,243,377,354,375,252,114,244,355,253,115,245,376,356,686,685,688,690,90,428,452,500,392,91,426,450,498,390,92,427,451,499,391,431,89,455,503,395,429,453,501,393,87,430,88,454,502,394,81,458,434,506,398,82,456,432,504,396,83,457,433,505,397,461,84,437,509,401,507,459,85,435,399,460,86,436,508,400,666,661,664,669,30,464,263,55,272,31,462,261,56,270,32,463,262,54,271,467,33,259,51,275,465,260,52,273,34,466,35,258,53,274,28,269,470,46,278,29,267,468,47,276,27,268,469,45,277,265,24,473,49,281,50,266,25,471,279,264,26,472,48,280,681,680,673,676,169,316,328,304,292,170,317,329,305,293,168,315,327,303,291,312,165,324,300,288,313,325,301,289,166,314,167,326,302,290,175,319,307,295,283,176,320,308,296,284,174,318,306,294,282,322,171,310,298,286,299,323,172,311,287,321,173,309,297,285,668,670,671,667,2,380,69,548,512,1,378,70,546,510,0,379,71,547,511,383,5,72,551,515,381,73,549,513,3,382,4,74,550,514,8,75,386,554,518,6,76,384,552,516,7,77,385,553,517,78,11,389,557,521,555,79,9,387,519,80,10,388,556,520,697,696,695,694,14,620,621,623,622,12,614,615,613,612,13,616,617,619,618,633,17,632,635,634,625,624,627,626,15,629,16,628,631,630,20,645,644,647,646,18,637,636,639,638,19,641,640,643,642,657,23,656,659,658,651,649,21,648,650,653,22,652,655,654,704,702,701,703,332,584,208,41,214,330,582,209,39,215,331,583,207,40,213,587,335,211,44,217,585,212,42,218,333,586,334,210,43,216,338,206,590,36,220,336,204,588,37,221,337,205,589,38,219,202,341,593,611,610,607,203,339,591,606,201,340,592,609,608,700,699,693,698,199,416,145,488,596,200,414,146,486,594,198,415,144,487,595,419,195,141,491,599,417,142,489,597,196,418,197,143,490,598,190,151,422,494,602,191,152,420,492,600,189,150,421,493,601,147,193,425,497,605,495,148,194,423,603,149,192,424,496,604,678,684,683,675,344,404,536,572,229,342,402,534,570,230,343,403,535,571,228,407,347,539,575,232,405,537,573,233,345,406,346,538,574,231,350,542,410,578,227,348,540,408,576,225,349,541,409,577,226,545,353,413,581,223,579,543,351,411,224,544,352,412,580,222,682,677,679,674,185,126,132,524,560,183,127,133,522,558,184,128,134,523,559,125,188,131,527,563,123,129,525,561,186,124,187,130,526,562,180,138,117,530,566,181,139,118,528,564,182,140,119,529,565,137,179,120,533,569,531,135,177,121,567,136,178,122,532,568,687,689,691,692 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#f4f724834d898f30c0a6fbb58eb0b496232f556dc00d71550d6e526db5e670b8, 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 21:47:09 · history