Equation 677 Database

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Magma 230fac362b99…

magma 230fac362b99
Size
705
Isomorphism class hash
230fac362b998b0a5582a0e66406fdf7a23323c91a565ed385bddfc0c99c2b1b
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 15:34:31
Display reorder
660,634,633,635,632,630,631,624,625,626,627,628,629,639,640,641,638,636,637,645,646,647,644,642,643,652,653,651,648,649,650,658,659,657,654,655,656,619,620,618,622,623,621,617,615,616,613,614,612,441,442,443,440,438,439,432,433,434,435,436,437,663,668,661,669,261,263,262,259,260,258,254,252,253,257,255,256,274,275,273,270,271,272,265,266,264,268,269,267,235,236,234,238,239,237,233,231,232,229,230,228,247,248,246,250,251,249,245,243,244,241,242,240,170,168,169,173,171,172,176,174,175,179,177,178,688,690,687,692,527,526,525,522,523,524,517,518,516,520,521,519,539,537,538,535,536,534,530,528,529,533,531,532,551,549,550,547,548,546,542,540,541,545,543,544,509,507,508,505,506,504,515,513,514,511,512,510,7,8,6,10,11,9,5,3,4,0,2,1,664,666,667,672,299,298,297,294,295,296,289,290,288,292,293,291,311,309,310,307,308,306,302,300,301,305,303,304,321,322,323,320,318,319,312,313,314,315,316,317,283,284,282,286,287,285,281,279,280,277,278,276,186,187,188,189,190,191,184,185,183,180,181,182,673,680,678,683,24,26,25,29,27,28,32,30,31,35,33,34,330,331,332,333,334,335,328,329,327,324,325,326,166,167,165,162,163,164,157,158,156,160,161,159,63,64,65,62,60,61,69,70,71,68,66,67,199,200,198,202,203,201,197,195,196,193,194,192,662,670,665,671,465,467,466,463,464,462,458,456,457,461,459,460,479,477,478,475,476,474,470,468,469,473,471,472,491,489,490,487,488,486,482,480,481,485,483,484,503,501,502,499,500,498,494,492,493,497,495,496,454,455,453,450,451,452,445,446,444,448,449,447,693,697,695,699,117,119,118,115,116,114,110,108,109,113,111,112,131,129,130,127,128,126,122,120,121,125,123,124,142,143,141,138,139,140,133,134,132,136,137,135,155,153,154,151,152,150,146,144,145,149,147,148,106,107,105,102,103,104,97,98,96,100,101,99,701,702,703,704,345,347,346,343,344,342,338,336,337,341,339,340,359,357,358,355,356,354,350,348,349,353,351,352,369,370,371,368,366,367,360,361,362,363,364,365,382,383,381,378,379,380,373,374,372,376,377,375,212,210,211,215,213,214,207,208,209,206,204,205,694,698,696,700,598,597,599,596,594,595,588,589,590,591,592,593,604,605,603,600,601,602,610,611,609,606,607,608,568,569,567,564,565,566,574,575,573,570,571,572,581,579,580,577,578,576,587,585,586,583,584,582,17,15,16,13,14,12,23,21,22,19,20,18,675,679,676,682,402,404,403,407,405,406,399,400,401,398,396,397,412,413,411,408,409,410,418,419,417,414,415,416,425,423,424,421,422,420,431,429,430,427,428,426,392,390,391,395,393,394,387,388,389,386,384,385,226,227,225,222,223,224,217,218,216,220,221,219,674,681,677,684,42,44,43,47,45,46,39,40,41,38,36,37,558,559,560,561,562,563,556,557,555,552,553,554,76,77,75,72,73,74,82,83,81,78,79,80,88,89,87,84,85,86,94,95,93,90,91,92,59,57,58,55,56,54,50,48,49,53,51,52,685,689,686,691 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, 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 15:34:38 · history