Equation 677 Database

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Magma bc7610835eb1…

magma bc7610835eb1
Size
705
Isomorphism class hash
bc7610835eb1ab2f413033e9e08448464c5de80ad6c840963795f178cea0139e
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 20:10:10
Display reorder
660,605,613,147,603,612,148,625,623,632,633,149,653,645,643,652,593,146,585,583,592,553,144,545,543,552,573,145,565,563,572,423,433,425,153,432,443,451,445,154,450,463,473,465,155,472,493,483,485,152,492,513,503,505,150,512,151,533,523,525,532,698,699,688,693,607,611,65,600,616,63,627,620,636,631,64,651,647,640,656,591,61,587,581,596,551,62,547,540,556,571,60,567,560,576,420,431,427,71,436,442,449,447,69,454,462,471,467,70,476,491,481,487,67,496,511,501,507,68,516,66,531,521,527,536,700,704,695,690,102,393,75,345,54,76,103,346,55,394,77,395,104,347,56,392,74,105,344,57,390,72,106,342,58,391,73,107,343,59,336,384,100,81,52,337,385,101,82,53,338,386,99,83,51,387,339,96,80,48,388,340,97,78,49,79,389,341,98,50,669,664,671,676,321,25,39,175,194,40,322,176,192,26,41,24,323,174,193,28,38,320,178,197,29,36,318,179,195,27,37,319,177,196,173,31,312,45,200,171,32,313,46,198,172,30,314,47,199,34,169,315,44,203,35,170,316,42,201,43,33,168,317,202,670,667,684,680,610,601,86,608,609,84,630,628,629,621,85,641,650,648,649,580,89,590,588,589,541,87,550,548,549,561,88,570,568,569,428,421,430,92,429,448,457,459,90,458,468,460,470,91,469,480,488,490,95,489,500,508,510,93,509,94,520,528,530,529,685,689,697,702,617,604,217,619,615,218,637,639,635,624,216,644,657,659,655,584,220,597,599,595,544,221,557,559,555,564,219,577,579,575,439,424,437,223,435,440,444,455,224,453,479,464,477,222,475,484,499,497,226,495,504,519,517,227,515,225,524,539,537,535,696,701,692,691,614,618,138,602,606,139,634,622,626,638,140,658,654,642,646,598,141,594,582,586,558,142,554,542,546,578,143,574,562,566,422,438,434,136,426,441,456,452,137,446,461,478,474,135,466,498,482,494,132,486,518,502,514,133,506,134,538,522,534,526,687,694,686,703,381,357,186,417,112,187,382,418,113,358,188,359,383,419,111,356,189,380,416,108,354,190,378,414,109,355,191,379,415,110,408,348,372,184,118,409,349,373,185,119,410,350,374,183,117,351,411,375,180,114,352,412,376,181,115,182,353,413,377,116,662,674,681,672,249,228,261,369,214,262,250,370,215,229,263,230,251,371,213,231,260,248,368,210,232,258,246,366,211,233,259,247,367,212,360,234,240,252,205,361,235,241,253,206,362,236,242,254,204,237,363,243,255,208,238,364,244,256,209,257,239,365,245,207,678,661,673,666,309,273,278,405,160,276,310,406,161,274,277,275,311,407,159,272,281,308,404,156,270,279,306,402,157,271,280,307,403,158,396,264,300,284,166,397,265,301,282,167,398,266,302,283,165,267,399,303,287,162,268,400,304,285,163,286,269,401,305,164,675,665,677,663,131,333,290,7,22,288,129,8,23,334,289,335,130,6,21,332,293,127,10,18,330,291,128,11,19,331,292,126,9,20,5,324,122,296,13,3,325,120,294,14,4,326,121,295,12,327,0,125,299,16,328,2,123,297,17,298,329,1,124,15,683,679,682,668 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#bc84586c53073a7227d3f1cff463f9e10a3c0feadba644a539b68478442af133, 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 20:10:11 · history