Equation 677 Database

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Magma bf0ec28d3fe7…

magma bf0ec28d3fe7
Size
705
Isomorphism class hash
bf0ec28d3fe7a9fd54f15c4ed23804f5c45a507b92ab72218b7adba330517c71
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 17:35:13
Display reorder
660,507,40,522,248,492,508,43,523,246,493,524,509,247,494,46,506,521,37,244,491,504,519,1,245,489,505,520,35,243,490,38,513,254,498,483,32,514,252,499,484,34,515,253,500,485,516,47,250,501,486,517,41,251,502,487,518,44,249,503,488,682,683,681,685,290,302,233,116,274,288,300,231,114,275,232,289,115,273,301,286,236,298,119,277,287,234,299,117,278,285,235,297,118,276,293,239,111,281,272,291,237,112,279,270,292,238,113,280,271,242,296,110,284,268,240,294,108,282,269,241,295,109,283,267,664,667,663,671,66,42,561,140,7,67,45,562,138,8,563,68,139,9,39,69,560,25,143,10,70,558,33,141,11,71,559,36,142,12,28,552,135,64,5,26,553,136,65,6,27,554,137,63,4,555,31,134,60,0,556,29,132,61,2,557,30,133,62,3,679,686,687,674,637,640,638,91,642,645,648,646,92,650,654,652,90,658,656,628,630,632,94,634,613,614,616,95,618,620,622,624,93,626,480,329,89,182,510,481,327,87,180,511,482,328,88,181,512,588,590,85,592,593,598,600,86,597,602,606,608,84,605,610,703,698,700,704,390,340,477,205,324,391,341,478,206,325,479,392,204,326,339,389,476,343,201,323,387,474,344,202,321,388,475,342,203,322,338,468,196,381,315,336,469,197,382,316,337,470,195,383,317,471,334,199,384,318,472,335,200,385,319,473,333,198,386,320,691,692,690,693,166,573,549,83,155,167,574,550,81,153,551,165,82,154,575,162,548,572,79,151,163,546,570,80,152,164,547,571,78,150,564,540,74,157,146,565,541,72,158,144,566,542,73,156,145,543,567,77,160,149,544,568,75,161,147,545,569,76,159,148,665,670,669,672,431,360,124,210,52,429,361,125,211,53,123,430,212,51,362,434,120,359,209,48,432,121,357,207,49,433,122,358,208,50,366,130,216,437,58,367,131,217,435,59,368,129,218,436,57,126,365,215,440,54,127,363,213,438,55,128,364,214,439,56,694,695,696,689,378,534,585,19,450,379,535,586,20,451,587,380,21,452,536,377,584,533,22,449,375,582,531,23,447,376,583,532,24,448,525,576,17,369,441,526,577,18,370,442,527,578,16,371,443,579,528,13,372,444,580,529,14,373,445,581,530,15,374,446,673,688,677,684,641,643,639,224,636,649,651,647,222,644,655,657,223,653,659,633,631,635,220,629,617,615,619,221,612,625,623,627,219,621,537,467,230,495,330,538,465,228,496,331,539,466,229,497,332,594,595,226,591,589,599,603,227,601,596,607,611,225,609,604,699,697,702,701,414,310,257,98,193,415,311,255,96,194,256,416,97,192,309,413,260,313,101,189,411,258,314,99,190,412,259,312,100,191,308,263,104,405,184,306,261,102,406,185,307,262,103,407,183,266,304,107,408,187,264,305,105,409,188,265,303,106,410,186,662,666,668,661,462,346,426,169,402,463,347,427,170,403,428,464,168,404,345,461,425,349,172,401,459,423,350,173,399,460,424,348,171,400,352,417,175,453,393,353,418,176,454,394,351,419,174,455,395,420,355,178,456,396,421,356,179,457,397,422,354,177,458,398,678,676,675,680 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#59c0dab3d55e83047c113809dcb6925b23956e0c747f2365bb6fbba97ebd5493, 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 17:35:15 · history