Equation 677 Database

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Magma 767a16c6528c…

magma 767a16c6528c
Size
705
Isomorphism class hash
767a16c6528c292d76aa321d140b781315b5ba55c99cfe7c21e53ccf11d6c46e
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 19:43:01
Display reorder
660,51,448,452,449,454,468,52,472,469,474,53,423,433,430,434,50,508,512,509,514,48,528,532,529,534,49,488,492,489,494,57,569,571,574,577,58,589,591,594,597,59,549,551,554,557,629,56,631,634,637,649,54,651,654,657,609,55,611,614,617,701,692,699,693,179,453,446,455,445,473,177,466,475,465,178,424,428,435,427,175,513,506,515,505,176,533,526,535,525,174,493,486,495,485,170,575,578,567,566,168,595,598,587,586,169,555,558,547,546,635,173,638,627,626,655,171,658,647,646,615,172,618,607,606,694,703,688,686,81,361,349,409,313,362,82,350,410,314,83,360,348,408,312,80,364,352,412,316,78,365,353,413,317,79,363,351,411,315,72,367,415,355,319,73,368,416,356,320,74,366,414,354,318,370,75,418,358,322,371,76,419,359,323,369,77,417,357,321,677,684,670,675,148,282,289,251,253,283,149,290,249,254,147,284,288,250,252,144,285,292,247,256,145,286,293,248,257,146,287,291,246,255,154,280,242,295,259,155,281,240,296,260,153,279,241,294,258,276,150,245,298,262,277,151,243,299,263,278,152,244,297,261,665,682,661,664,107,440,457,458,456,460,105,477,478,476,106,426,437,438,436,103,504,516,518,517,104,524,537,539,538,102,484,496,498,497,98,561,576,570,560,96,580,596,590,581,97,541,556,550,540,621,101,636,630,620,641,99,656,650,640,601,100,616,610,600,690,698,695,700,1,459,444,450,451,479,0,464,470,471,2,439,425,431,432,3,519,503,510,511,4,536,523,530,531,5,499,483,490,491,6,579,572,565,573,7,599,592,585,593,8,559,552,545,553,639,9,632,625,633,659,10,652,645,653,619,11,612,605,613,704,687,691,689,35,447,441,442,443,467,33,461,462,463,34,429,420,421,422,31,507,500,501,502,32,527,521,520,522,30,487,480,481,482,26,568,563,562,564,24,588,583,582,584,25,548,543,542,544,628,29,623,622,624,648,27,643,642,644,608,28,603,602,604,685,697,702,696,94,157,301,385,265,158,95,302,386,266,93,156,300,384,264,90,160,304,388,268,91,161,305,389,269,92,159,303,387,267,85,163,391,307,271,86,164,392,308,272,84,162,390,306,270,166,88,394,310,274,167,89,395,311,275,165,87,393,309,273,672,681,663,668,60,337,134,397,44,338,61,132,398,42,62,336,133,396,43,63,340,137,400,47,64,341,135,401,45,65,339,136,399,46,66,343,403,140,39,67,344,404,138,40,68,342,402,139,41,346,69,406,143,38,347,70,407,141,36,345,71,405,142,37,674,683,669,662,233,222,183,203,325,223,231,184,201,326,232,224,185,202,324,229,225,182,199,328,230,226,180,200,329,228,227,181,198,327,239,220,194,189,331,237,221,192,190,332,238,219,193,191,330,216,235,197,188,334,217,236,195,186,335,218,234,196,187,333,667,678,671,680,14,121,373,208,114,122,12,374,209,115,13,120,372,207,116,17,124,376,204,117,15,125,377,205,118,16,123,375,206,119,20,127,214,379,112,18,128,215,380,113,19,126,213,378,111,130,23,210,382,108,131,21,211,383,109,129,22,212,381,110,673,666,676,679 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#a559a3aef5c48d7617a1f37068ce834508ecbb6c78b3262065881b6dd2cda018, 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 19:43:02 · history