Equation 677 Database

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Magma 9785abeebe28…

magma 9785abeebe28
Size
705
Isomorphism class hash
9785abeebe283f00b385a8575389a41eaf3ef531bb0d21953983990faf11d47e
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 18:23:00
Display reorder
660,91,502,511,507,516,522,527,92,531,536,482,487,90,491,496,423,94,431,427,436,449,95,451,450,453,463,93,471,467,476,89,631,622,627,636,87,651,642,647,656,88,611,602,607,616,551,85,542,547,556,571,86,562,567,576,591,84,582,587,596,698,685,699,691,189,509,508,510,512,529,530,190,528,532,489,490,191,488,492,429,188,428,430,432,457,186,456,458,446,469,187,468,470,472,180,628,629,630,632,181,648,649,650,652,182,608,609,610,612,548,183,549,550,552,568,184,569,570,572,588,185,589,590,592,692,690,689,697,157,412,328,352,316,413,353,158,329,317,411,351,156,327,315,408,160,324,348,312,409,161,325,349,313,410,159,326,350,314,163,334,418,358,322,164,335,419,359,323,162,333,417,357,321,330,166,414,354,318,331,167,415,355,319,332,165,416,356,320,667,671,681,668,16,127,376,292,230,128,293,17,377,228,126,291,15,375,229,130,12,372,288,233,131,13,373,289,231,129,14,374,290,232,22,382,125,298,236,23,383,123,299,234,21,381,124,297,235,378,18,121,294,239,379,19,122,295,237,380,20,120,296,238,666,664,679,675,31,505,504,500,515,525,520,33,524,535,485,480,35,484,495,425,28,424,421,435,445,25,444,443,447,465,27,464,460,475,42,624,625,621,635,44,644,645,640,655,47,604,605,601,615,544,41,545,541,555,564,36,565,561,575,584,38,585,580,595,695,703,696,702,100,518,517,519,503,538,539,101,537,523,497,499,99,498,483,437,96,438,439,422,441,97,440,442,448,477,98,478,479,462,106,638,637,639,623,107,657,658,659,643,105,618,617,619,603,557,102,558,559,543,577,103,578,579,563,598,104,597,599,583,686,701,688,687,244,506,514,501,513,526,521,245,534,533,486,481,243,494,493,426,240,434,420,433,455,241,459,454,452,466,242,474,461,473,250,634,626,620,633,251,654,646,641,653,249,614,606,600,613,554,246,546,540,553,574,247,566,560,573,594,248,586,581,593,700,704,693,694,154,176,63,304,134,174,305,155,64,132,175,303,153,65,133,179,150,62,300,137,177,151,60,301,135,178,152,61,302,136,145,69,171,310,140,146,70,172,311,138,144,71,173,309,139,68,148,170,306,143,66,149,168,307,141,67,147,169,308,142,673,665,674,682,6,117,400,221,388,118,219,7,401,389,119,220,8,399,387,116,9,396,217,384,114,10,397,218,385,115,11,398,216,386,4,406,108,227,394,5,407,109,225,395,3,405,110,226,393,402,1,111,223,390,403,0,112,224,391,404,2,113,222,392,678,683,684,680,43,340,280,194,80,341,192,45,281,78,339,193,46,279,79,336,40,276,197,83,337,37,277,195,81,338,39,278,196,82,24,286,346,200,75,26,287,347,198,76,29,285,345,199,77,282,30,342,203,74,283,32,343,201,72,284,34,344,202,73,670,676,669,663,49,268,205,364,255,269,365,50,206,256,267,363,48,204,257,264,52,208,360,254,265,53,209,361,252,266,51,207,362,253,55,211,274,370,261,56,212,275,371,262,54,210,273,369,263,214,58,270,366,260,215,59,271,367,258,213,57,272,368,259,661,672,662,677 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#7eb365a46a73bc671c535e7eab37a7fd590c6d5c6b4c14d45f700003c9150a2d, 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 18:23:01 · history