Equation 677 Database

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Magma ef5303eff015…

magma ef5303eff015
Size
705
Isomorphism class hash
ef5303eff01516bffe35f7980565511e5ddaa8e9c8bf84868f7f7d5a7a7442f4
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 16:48:36
Display reorder
660,542,514,158,462,438,543,515,159,463,439,541,513,160,461,437,510,538,161,458,434,162,539,511,459,435,512,540,163,460,436,533,505,164,453,429,534,506,165,454,430,532,504,166,452,428,508,536,167,456,432,509,537,168,457,433,507,535,169,455,431,681,679,683,685,366,402,247,197,187,367,403,245,198,185,365,401,246,199,186,398,362,243,196,183,244,363,399,194,184,400,364,242,195,182,357,393,238,203,193,358,394,236,204,191,356,392,237,205,192,396,360,241,202,189,397,361,239,200,190,395,359,240,201,188,672,668,664,663,414,342,171,490,258,415,343,172,491,259,413,341,170,489,257,338,410,174,486,254,175,411,339,487,255,340,412,173,488,256,405,333,177,481,249,406,334,178,482,250,404,332,176,480,248,336,408,180,484,252,337,409,181,485,253,335,407,179,483,251,682,673,677,678,646,650,145,644,648,654,658,143,653,656,638,642,144,636,640,618,614,141,612,616,142,622,626,621,624,634,630,140,629,632,126,545,136,129,465,124,546,134,127,466,125,544,135,128,464,599,597,139,600,601,610,604,137,605,608,547,123,138,1,467,703,697,700,704,42,216,63,390,354,43,214,64,391,355,44,215,65,389,353,219,41,66,386,350,67,39,217,387,351,218,40,68,388,352,48,211,69,381,345,49,212,70,382,346,50,213,71,380,344,210,47,72,384,348,208,45,73,385,349,209,46,74,383,347,692,691,689,694,502,16,118,426,330,503,17,119,427,331,501,18,117,425,329,15,498,121,422,326,122,499,13,423,327,14,500,120,424,328,493,22,116,417,321,494,23,114,418,322,492,24,115,416,320,21,496,112,420,324,19,497,113,421,325,20,495,111,419,323,665,662,661,667,294,52,221,283,268,295,53,222,281,266,293,51,220,282,267,55,290,224,279,271,225,291,56,280,269,54,292,223,278,270,285,58,227,274,263,286,59,228,272,264,284,57,226,273,265,61,288,230,277,262,62,289,231,275,260,60,287,229,276,261,693,695,696,690,450,306,32,530,594,451,307,30,531,595,449,305,31,529,593,302,446,28,526,590,29,447,303,527,591,304,448,27,528,592,441,297,38,521,585,442,298,36,522,586,440,296,37,520,584,300,444,34,524,588,301,445,35,525,589,299,443,33,523,587,684,688,675,680,647,651,4,649,645,655,659,5,657,652,639,643,6,641,637,619,615,3,617,613,0,623,627,625,620,635,631,2,633,628,234,570,10,517,132,232,568,11,518,130,233,569,12,516,131,603,602,9,598,596,611,607,7,609,606,571,235,8,519,133,699,698,702,701,565,564,88,478,582,567,566,89,479,583,563,562,87,477,581,556,557,91,474,578,92,559,558,475,579,561,560,90,476,580,25,207,94,469,573,549,548,95,470,574,26,206,93,468,572,552,553,97,472,576,554,555,98,473,577,551,550,96,471,575,666,671,670,669,318,378,155,80,103,319,379,156,78,104,317,377,157,79,102,374,314,154,76,99,152,315,375,77,100,376,316,153,75,101,309,369,146,86,109,310,370,147,84,110,308,368,148,85,108,372,312,149,82,105,373,313,150,83,106,371,311,151,81,107,686,674,687,676 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#3f4c16e16e9bd422beeb4e3c1331ed0b07b0ac931af0d47b2d7497fadfe20a6b, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 16:48:37 · history