Equation 677 Database

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Magma c310ab0a743b…

magma c310ab0a743b
Size
705
Isomorphism class hash
c310ab0a743b18eb2d4a4cd8faade4de5a3495b80c519dc10c09b5e6040ce309
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 19:55:36
Display reorder
660,116,192,50,381,506,117,193,51,382,507,118,191,52,380,505,195,115,49,377,502,196,113,47,378,503,194,114,48,379,504,122,190,41,387,512,123,188,42,388,513,124,189,43,386,511,186,121,44,383,508,187,119,45,384,509,185,120,46,385,510,662,665,670,661,224,356,328,339,341,225,357,326,340,342,226,358,327,338,343,355,223,324,335,344,353,221,325,336,345,354,222,323,337,346,230,362,319,330,347,231,363,317,331,348,232,364,318,329,349,361,229,322,333,350,359,227,320,334,351,360,228,321,332,352,685,687,689,690,92,165,215,142,154,93,166,216,140,152,94,164,217,141,153,161,91,218,138,150,162,89,219,139,151,163,90,220,137,149,98,171,213,148,160,99,172,214,146,158,100,170,212,147,159,167,97,209,144,156,168,95,210,145,157,169,96,211,143,155,664,667,669,672,238,542,369,441,470,236,543,370,442,471,237,541,368,440,469,538,234,365,437,466,539,235,366,438,467,540,233,367,439,468,244,548,375,447,476,242,549,376,448,477,243,547,374,446,475,544,240,371,443,472,545,241,372,444,473,546,239,373,445,474,677,679,682,674,246,458,566,518,590,247,459,567,519,591,245,457,565,517,589,454,249,562,514,586,455,250,563,515,587,456,248,564,516,588,252,464,572,524,596,253,465,573,525,597,251,463,571,523,595,460,255,568,520,592,461,256,569,521,593,462,254,570,522,594,666,671,663,668,129,494,429,206,530,130,495,430,207,531,128,493,428,208,529,490,125,425,205,526,491,126,426,203,527,492,127,427,204,528,135,500,435,197,536,136,501,436,198,537,134,499,434,199,535,496,131,431,200,532,497,132,432,201,533,498,133,433,202,534,693,698,696,695,80,598,599,453,28,81,634,635,632,633,82,600,601,452,27,602,79,603,449,24,604,77,605,450,25,607,78,606,451,26,86,654,655,653,652,87,659,658,657,656,88,650,651,649,648,638,85,639,637,636,643,83,642,641,640,647,84,646,645,644,701,702,703,704,55,405,264,616,617,53,406,265,619,618,54,404,263,614,615,401,58,267,608,609,402,56,268,611,610,403,57,266,613,612,61,411,262,629,628,59,412,260,631,630,60,410,261,626,627,407,64,258,620,621,408,62,259,623,622,409,63,257,625,624,700,699,694,697,29,417,578,482,393,30,418,579,483,394,31,416,577,481,392,413,32,574,478,389,414,33,575,479,390,415,34,576,480,391,35,423,584,488,399,36,424,585,489,400,37,422,583,487,398,419,38,580,484,395,420,39,581,485,396,421,40,582,486,397,680,675,676,683,65,281,296,314,279,66,282,297,315,280,67,283,298,316,278,284,68,295,313,275,285,69,293,311,276,286,70,294,312,277,71,287,302,305,270,72,288,303,306,271,73,289,304,307,269,290,74,301,308,273,291,75,299,309,274,292,76,300,310,272,678,684,673,681,7,17,554,177,101,8,15,555,178,102,6,16,553,176,103,13,10,550,173,104,14,11,551,174,105,12,9,552,175,106,5,23,560,183,107,3,21,561,184,108,4,22,559,182,109,19,0,556,179,110,20,2,557,180,111,18,1,558,181,112,686,688,691,692 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#b3dac6ff36f26cacc8049b7c1e09fd794a0277a3d237510b4c6377f158398334, 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 19:55:37 · history