Equation 677 Database

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Magma b40428749146…

magma b40428749146
Size
705
Isomorphism class hash
b404287491469797d278d14518869bdd2aaedcb9725374aefc959a0c04bb837e
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 17:42:10
Display reorder
660,515,2,501,513,507,535,527,1,521,533,495,487,0,480,493,5,435,426,427,433,3,453,448,449,452,4,475,466,467,473,627,8,635,626,633,6,655,646,647,653,7,615,606,607,613,555,11,546,547,553,575,9,566,567,573,595,10,586,587,593,685,699,695,686,511,30,514,508,512,531,532,31,534,528,491,492,32,494,488,33,431,432,434,428,34,457,458,459,446,35,471,472,474,468,634,28,631,632,628,29,651,652,654,648,27,611,612,614,608,551,24,552,554,548,571,25,572,574,568,591,26,592,594,588,690,693,687,694,304,247,388,128,352,305,353,248,389,126,303,351,246,387,127,250,300,348,384,131,251,301,349,385,129,249,302,350,386,130,394,245,310,358,123,243,311,359,395,124,244,309,357,393,125,306,241,354,390,122,307,242,355,391,120,308,240,356,392,121,665,670,662,676,188,50,197,73,209,186,207,48,195,74,187,208,49,196,72,53,191,205,193,76,51,189,206,194,77,52,190,204,192,75,203,56,183,215,79,54,184,213,201,80,55,185,214,202,78,182,59,211,199,82,180,57,212,200,83,181,58,210,198,81,663,680,674,671,500,99,502,516,503,520,523,100,522,536,481,483,101,482,496,98,421,422,420,436,96,443,445,444,447,97,460,462,461,476,621,105,620,622,636,106,641,642,640,656,107,600,602,601,616,540,104,542,541,556,560,102,562,561,576,581,103,582,580,596,700,702,698,703,517,221,519,509,518,537,538,219,539,529,497,498,220,499,489,217,437,438,439,429,218,440,441,442,450,216,478,477,479,469,639,227,638,637,629,225,657,658,659,649,226,618,617,619,609,557,223,558,559,549,577,224,578,579,569,598,222,597,599,589,696,689,688,701,505,168,506,510,504,525,524,169,526,530,485,484,170,486,490,171,424,423,425,430,172,455,454,456,451,173,464,463,465,470,625,174,624,623,630,175,644,643,645,650,176,604,603,605,610,544,177,543,545,550,564,178,563,565,570,584,179,583,585,590,692,704,691,697,116,45,139,84,340,114,341,46,140,85,115,339,47,138,86,44,119,336,142,87,42,117,337,143,88,43,118,338,141,89,137,36,111,346,90,37,112,347,135,91,38,113,345,136,92,110,39,342,133,93,108,40,343,134,94,109,41,344,132,95,681,669,666,677,412,19,364,69,316,413,317,20,365,70,411,315,18,363,71,22,408,312,360,68,23,409,313,361,66,21,410,314,362,67,370,17,418,322,60,15,419,323,371,61,16,417,321,369,62,414,13,318,366,63,415,14,319,367,64,416,12,320,368,65,679,667,684,672,284,229,292,376,256,282,257,230,293,377,283,255,228,291,375,232,287,252,288,372,233,285,253,289,373,231,286,254,290,374,298,235,279,262,382,236,280,263,299,383,234,281,261,297,381,278,238,258,294,378,276,239,259,295,379,277,237,260,296,380,683,682,673,661,400,151,265,328,156,401,157,152,266,329,399,158,150,264,327,154,396,159,268,324,155,397,160,269,325,153,398,161,267,326,271,149,406,162,334,147,407,163,272,335,148,405,164,270,333,402,145,165,274,330,403,146,166,275,331,404,144,167,273,332,678,675,668,664 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#6086f0079822f3fde2aa4f203419cd6117656c7d05938f081a69b332c89c02c3, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 17:42:11 · history