Equation 677 Database

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Magma 746b6428b785…

magma 746b6428b785
Size
705
Isomorphism class hash
746b6428b785f568202cd1baa0996440a9c6eae5913879b742eb526f95fcd3b9
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 20:33:51
Display reorder
660,136,464,460,471,461,137,430,428,426,421,135,445,441,452,444,132,525,520,532,524,133,485,481,492,484,134,505,501,512,504,142,585,580,592,582,143,545,541,552,542,141,565,561,572,562,645,138,641,652,642,605,139,601,612,602,625,140,621,632,622,691,686,700,699,21,469,470,472,463,22,424,425,427,420,23,450,451,453,443,20,530,531,533,523,18,490,491,493,483,19,510,511,513,503,12,590,591,593,584,13,550,551,553,544,14,570,571,573,564,650,15,651,653,644,610,16,611,613,604,630,17,631,633,624,692,689,694,698,259,181,80,338,174,260,182,78,336,175,258,180,79,337,176,262,184,83,341,177,263,185,81,339,178,261,183,82,340,179,257,187,75,344,172,255,188,76,342,173,256,186,77,343,171,190,253,74,347,168,191,254,72,345,169,189,252,73,346,170,671,670,662,681,110,410,0,290,386,108,408,2,288,384,109,409,1,289,385,113,413,4,293,389,111,411,5,291,387,112,412,3,292,388,116,416,7,296,392,114,414,8,294,390,115,415,6,295,391,419,119,10,299,395,417,117,11,297,393,418,118,9,298,394,664,678,683,673,61,468,462,475,474,62,432,429,435,434,60,449,442,459,458,64,529,522,539,538,65,489,482,499,498,63,509,502,519,518,67,589,583,599,598,68,549,543,559,558,66,569,563,579,578,649,70,643,659,658,609,71,603,619,618,629,69,623,639,638,701,690,685,703,121,478,476,477,479,122,438,436,437,439,120,456,454,440,457,124,536,534,521,537,125,496,494,480,497,123,516,514,500,517,127,596,594,581,597,128,556,554,540,557,126,576,574,560,577,656,130,654,640,657,616,131,614,600,617,636,129,634,620,637,702,697,696,687,102,466,467,473,465,103,422,423,433,431,104,447,448,455,446,105,527,528,535,526,106,487,488,495,486,107,507,508,515,506,100,587,588,595,586,101,547,548,555,546,99,567,568,575,566,647,96,648,655,646,607,97,608,615,606,627,98,628,635,626,695,688,704,693,92,39,362,314,35,90,40,360,312,33,91,41,361,313,34,95,38,365,317,31,93,36,363,315,32,94,37,364,316,30,87,45,368,320,26,88,46,366,318,24,89,47,367,319,25,44,86,371,323,29,42,84,369,321,27,43,85,370,322,28,667,679,675,676,244,144,158,302,374,245,145,156,300,372,243,146,157,301,373,240,147,161,305,377,241,148,159,303,375,242,149,160,304,376,250,150,164,308,380,251,151,162,306,378,249,152,163,307,379,153,246,167,311,383,154,247,165,309,381,155,248,166,310,382,665,677,666,684,198,326,266,398,278,199,324,264,396,276,200,325,265,397,277,201,329,269,401,281,202,327,267,399,279,203,328,268,400,280,196,332,272,404,284,197,330,270,402,282,195,331,271,403,283,335,192,275,407,287,333,193,273,405,285,334,194,274,406,286,680,663,669,661,205,231,59,350,227,206,232,57,348,225,204,233,58,349,226,208,230,55,353,223,209,228,56,351,224,207,229,54,352,222,211,237,50,356,218,212,238,48,354,216,210,239,49,355,217,236,214,53,359,221,234,215,51,357,219,235,213,52,358,220,672,674,682,668 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#c2d2ffbf4b11c3cb3cbc2e9e264bf213176e8d1ad1040891146c21601605ebcd, 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 20:33:53 · history