Equation 677 Database

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Magma 89a7c2e02839…

magma 89a7c2e02839
Size
705
Isomorphism class hash
89a7c2e028394a8197ebb58964ebfbff5fb87115f4d11fd8c248311a402ec6cb
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 19:58:09
Display reorder
660,304,383,82,87,216,305,384,83,88,214,306,382,81,89,215,386,307,78,86,219,387,308,79,84,217,385,309,80,85,218,310,381,73,93,211,311,379,74,94,212,312,380,72,95,213,377,313,76,92,210,378,314,77,90,208,376,315,75,91,209,668,666,663,669,57,407,351,355,365,58,408,349,356,366,59,406,350,357,364,410,56,347,354,368,411,54,348,352,369,409,55,346,353,367,48,405,342,361,371,49,403,340,362,372,50,404,341,363,370,401,51,345,360,374,402,52,343,358,375,400,53,344,359,373,688,687,686,685,99,479,450,335,241,100,480,448,336,242,101,478,449,334,243,482,98,453,338,240,483,96,451,339,238,481,97,452,337,239,105,477,456,333,232,106,475,454,331,233,107,476,455,332,234,473,104,459,329,235,474,102,457,330,236,472,103,458,328,237,661,664,670,662,18,431,2,467,42,19,432,1,468,43,20,430,0,466,44,434,21,5,470,45,435,22,3,471,46,433,23,4,469,47,16,429,8,465,40,17,427,6,463,41,15,428,7,464,39,425,12,11,461,36,426,13,9,462,37,424,14,10,460,38,676,678,674,677,148,587,510,586,419,149,588,508,589,420,150,585,509,584,418,593,151,513,592,422,594,152,511,595,423,591,153,512,590,421,154,582,516,583,417,155,578,514,579,415,156,580,515,581,416,575,157,519,574,413,577,158,517,576,414,572,159,518,573,412,672,665,671,667,66,230,491,503,319,67,231,492,504,320,68,229,490,502,321,226,69,494,506,318,227,70,495,507,316,228,71,493,505,317,64,221,489,501,325,65,222,487,499,326,63,220,488,500,327,224,60,485,497,324,225,61,486,498,322,223,62,484,496,323,695,698,693,694,114,120,571,141,563,115,646,647,645,644,116,121,570,140,562,653,117,655,654,652,657,118,659,658,656,648,119,651,650,649,112,125,569,144,557,113,126,567,142,558,111,127,568,143,556,124,108,565,147,560,122,109,566,145,561,123,110,564,146,559,703,701,702,704,170,527,539,635,634,171,528,540,636,637,169,526,538,633,632,530,166,542,641,640,531,167,543,642,643,529,168,541,639,638,161,525,537,630,631,162,523,535,626,627,160,524,536,628,629,521,164,533,622,623,522,165,534,625,624,520,163,532,620,621,700,699,696,697,302,610,611,443,205,303,613,612,444,206,301,608,609,442,207,616,298,617,446,204,619,299,618,447,202,614,300,615,445,203,293,607,606,441,196,294,603,602,439,197,292,605,604,440,198,599,296,598,437,199,600,297,601,438,200,597,295,596,436,201,675,680,684,683,399,172,133,33,551,397,173,131,34,552,398,174,132,35,550,175,395,129,32,554,176,396,130,30,555,177,394,128,31,553,390,178,139,24,549,388,179,137,25,547,389,180,138,26,548,181,393,135,27,545,182,391,136,28,546,183,392,134,29,544,681,679,682,673,193,254,261,279,284,194,255,259,277,285,195,253,260,278,283,250,192,257,275,280,251,190,258,276,281,252,191,256,274,282,184,245,267,270,290,185,246,265,268,291,186,244,266,269,289,248,187,263,273,286,249,188,264,271,287,247,189,262,272,288,689,690,692,691 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#b82bea23d952545bcb5d6b6a0cc235694bb3bc5cc3b3a153b6c38e307d02b955, 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 19:58:10 · history