Equation 677 Database

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Magma b66925742c40…

magma b66925742c40
Size
705
Isomorphism class hash
b66925742c40517aefa21c17d7f45c355e3d17cbda92d60eaf35cc1b94399bb7
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 17:34:00
Display reorder
660,23,610,605,616,601,21,621,630,625,636,22,641,650,645,656,19,590,580,585,596,20,550,541,545,556,18,570,561,565,576,426,14,430,424,434,12,450,441,445,456,13,470,460,465,476,490,17,480,485,496,510,15,500,505,516,530,16,520,525,536,687,704,688,686,94,606,614,618,611,95,631,626,634,638,93,651,646,654,658,90,586,591,594,598,91,546,551,554,558,92,566,571,574,578,433,85,427,431,436,86,446,451,454,458,84,466,471,474,478,486,88,491,494,498,506,89,511,514,518,526,87,531,534,538,697,689,701,693,167,405,237,345,321,165,322,406,238,346,166,323,407,239,347,163,404,320,236,344,164,402,318,234,342,162,403,319,235,343,228,158,396,312,336,156,397,313,229,337,157,398,314,230,338,399,161,315,231,339,400,159,316,232,340,401,160,317,233,341,683,673,675,664,63,273,225,309,27,64,28,274,226,310,65,29,275,227,311,62,272,26,224,308,60,270,24,222,306,61,271,25,223,307,216,69,264,33,300,70,265,34,217,301,71,266,35,218,302,267,68,32,219,303,268,66,30,220,304,269,67,31,221,305,667,678,671,663,146,607,619,608,617,144,637,627,639,628,145,657,647,659,648,149,587,597,599,588,147,547,557,559,548,148,567,577,579,568,439,152,428,435,429,150,447,457,459,448,151,467,477,479,468,487,155,497,499,488,507,153,517,519,508,527,154,537,539,528,702,699,694,691,114,612,603,615,602,115,622,632,623,635,116,642,652,643,655,117,592,582,583,595,118,552,542,543,555,119,572,562,563,575,438,112,421,420,422,113,452,442,443,455,111,472,462,463,475,492,108,482,483,495,512,109,502,503,515,532,110,522,523,535,690,703,696,700,101,613,609,600,604,99,624,633,629,620,100,644,653,649,640,97,593,584,589,581,98,553,544,549,540,96,573,564,569,560,437,107,432,425,423,105,453,444,449,440,106,473,464,469,461,493,103,484,489,481,513,104,504,509,501,533,102,524,529,521,692,695,698,685,80,201,417,190,249,78,250,202,418,191,79,251,203,419,189,83,200,248,416,186,81,198,246,414,187,82,199,247,415,188,408,75,192,240,181,76,193,241,409,182,77,194,242,410,180,195,74,243,411,184,196,72,244,412,185,197,73,245,413,183,661,665,662,684,129,59,261,285,297,130,298,57,262,286,131,299,58,263,287,128,55,296,260,284,126,56,294,258,282,127,54,295,259,283,252,120,50,288,276,121,48,289,253,277,122,49,290,254,278,53,123,291,255,279,51,124,292,256,280,52,125,293,257,281,676,670,668,666,204,369,393,46,333,205,334,370,394,47,206,335,371,395,45,207,368,332,392,42,208,366,330,390,43,209,367,331,391,44,384,210,360,324,37,211,361,325,385,38,212,362,326,386,36,363,213,327,387,40,364,214,328,388,41,365,215,329,389,39,680,674,672,682,176,357,135,381,7,174,8,358,136,382,175,6,359,137,383,179,356,10,134,380,177,354,11,132,378,178,355,9,133,379,141,171,348,5,372,172,349,3,142,373,173,350,4,143,374,351,170,0,140,375,352,168,2,138,376,353,169,1,139,377,677,669,681,679 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#58f4898eb0f0372a4c749060353e7621900aa789e1d944064f9989e660cee0fd, 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 17:34:01 · history