Equation 677 Database

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Magma ca0aa7b2ac0c…

magma ca0aa7b2ac0c
Size
705
Isomorphism class hash
ca0aa7b2ac0cffc15984f3a04ffeec6bec7bd631c5ad415a328ce3c16fb50965
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 17:21:27
Display reorder
660,570,572,561,574,256,257,592,590,581,594,255,552,550,541,554,630,252,632,620,634,650,253,652,640,654,254,610,612,600,614,520,262,530,532,534,263,490,492,480,494,261,510,512,500,514,444,258,445,440,446,468,259,470,461,472,428,260,430,420,432,692,697,689,687,576,571,575,564,117,118,591,596,595,584,119,551,556,555,544,636,116,631,635,624,656,114,651,655,644,115,616,611,615,604,535,108,536,531,524,109,496,491,495,484,110,516,511,515,504,456,111,454,447,443,474,112,469,473,464,434,113,429,433,424,702,695,686,696,144,158,132,120,46,47,156,145,133,121,45,157,146,134,122,147,42,161,135,123,148,43,159,136,124,44,149,160,137,125,138,37,150,164,126,38,151,162,139,127,36,152,163,140,128,153,40,167,141,129,154,41,165,142,130,155,39,166,143,131,666,674,680,678,391,343,297,278,58,59,344,392,298,276,57,342,390,299,277,394,54,346,296,281,395,55,347,294,279,56,393,345,295,280,288,49,389,341,284,50,387,339,289,282,48,388,340,290,283,385,52,337,291,287,386,53,338,292,285,384,51,336,293,286,662,679,668,673,560,578,569,563,4,5,598,580,589,583,3,558,540,549,543,621,1,638,629,623,641,0,658,649,643,2,601,618,609,603,529,10,521,538,523,11,481,498,489,483,9,501,518,509,503,441,6,449,453,450,460,7,476,467,463,421,8,436,427,423,704,691,699,693,566,573,579,565,249,250,593,586,599,585,251,553,546,559,545,626,248,633,639,625,646,246,653,659,645,247,606,613,619,605,539,240,526,533,525,241,486,493,499,485,242,506,513,519,505,452,243,455,457,451,466,244,471,477,465,426,245,431,437,425,694,701,690,703,568,567,562,577,266,264,587,588,582,597,265,547,548,542,557,628,269,627,622,637,648,267,647,642,657,268,608,607,602,617,522,272,528,527,537,270,488,487,482,497,271,508,507,502,517,458,275,459,442,448,479,273,478,462,475,438,274,439,422,435,698,700,688,685,331,367,307,379,12,13,368,332,308,380,14,366,330,306,378,334,15,370,310,382,335,16,371,311,383,17,333,369,309,381,305,18,329,365,377,19,327,363,303,375,20,328,364,304,376,325,21,361,301,373,326,22,362,302,374,324,23,360,300,372,672,661,670,665,196,204,229,216,69,70,205,197,230,217,71,206,195,228,218,192,68,207,232,219,193,66,208,233,220,67,194,209,231,221,235,60,202,210,222,61,203,211,236,223,62,201,212,234,224,198,63,213,238,225,199,64,214,239,226,200,65,215,237,227,684,664,682,676,27,403,169,355,88,89,404,28,170,356,87,402,29,168,354,26,84,406,172,358,24,85,407,173,359,86,25,405,171,357,175,94,33,401,353,95,34,399,176,351,93,35,400,174,352,32,90,397,178,349,30,91,398,179,350,31,92,396,177,348,669,683,675,681,319,183,415,74,98,96,184,320,416,72,97,185,318,414,73,322,101,182,418,77,323,99,180,419,75,100,321,181,417,76,413,104,317,189,80,102,315,190,411,78,103,316,191,412,79,313,107,188,409,83,314,105,186,410,81,312,106,187,408,82,671,677,667,663 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#4f5c530836fd0cc12915654d9cb933b30b1ebf0f1cb96882ec953efd42c5ac65, 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 17:21:28 · history