Equation 677 Database

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Magma 36ff9b32a8b5…

magma 36ff9b32a8b5
Size
705
Isomorphism class hash
36ff9b32a8b5ac481e7767a2b66eae7ebc50e889188ae3dc476e65fb7f672164
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 21:55:49
Display reorder
660,572,35,571,569,562,589,33,592,591,582,552,34,551,549,542,31,632,631,629,622,32,652,651,649,642,30,612,611,609,602,532,531,26,529,521,492,491,24,489,480,512,511,25,509,501,445,446,29,444,441,471,472,27,469,462,431,432,28,429,421,688,686,691,690,575,203,564,568,574,588,201,595,584,594,555,202,544,548,554,199,635,624,628,634,200,655,644,648,654,198,615,604,608,614,535,524,194,528,534,495,484,192,488,494,515,504,193,508,514,451,457,197,443,447,464,475,195,468,474,424,435,196,428,434,689,695,700,697,184,207,319,23,54,21,208,185,320,55,183,209,318,22,56,206,180,322,19,57,204,181,323,20,58,205,182,321,18,59,190,317,213,14,52,191,315,214,12,53,189,316,215,13,51,313,186,212,17,48,314,187,210,15,49,312,188,211,16,50,661,662,683,666,391,158,355,89,75,87,156,392,356,76,390,157,354,88,77,161,394,358,85,74,159,395,359,86,72,160,393,357,84,73,389,353,164,95,81,387,351,162,93,82,388,352,163,94,83,349,385,167,91,80,350,386,165,92,78,348,384,166,90,79,684,675,673,669,561,270,576,565,570,585,271,580,596,590,541,272,556,545,550,273,621,636,625,630,274,640,656,645,650,275,601,616,605,610,522,536,268,525,530,482,496,269,485,490,502,516,267,505,510,448,440,264,452,455,476,461,265,465,470,436,422,266,425,430,694,692,704,702,566,149,573,560,567,581,147,586,593,587,546,148,553,540,547,145,626,633,620,627,146,646,653,641,647,144,606,613,600,607,526,533,155,520,527,486,493,153,481,487,506,513,154,500,507,456,453,151,450,454,473,466,152,460,467,433,426,150,420,427,685,701,696,693,579,96,578,577,563,597,97,598,599,583,558,98,559,557,543,99,639,638,637,623,100,658,659,657,643,101,619,618,617,603,538,539,102,537,523,498,499,103,497,483,518,519,104,517,503,459,458,105,449,442,478,479,106,477,463,439,438,107,437,423,687,703,698,699,250,6,230,227,415,225,7,251,228,416,249,8,229,226,414,9,246,233,223,418,10,247,231,224,419,11,248,232,222,417,241,236,4,218,413,242,234,5,216,411,240,235,3,217,412,239,244,1,221,409,237,245,0,219,410,238,243,2,220,408,671,679,681,674,137,288,283,331,116,332,289,135,284,114,136,290,282,330,115,291,133,286,334,119,292,134,287,335,117,293,132,285,333,118,143,281,294,329,111,141,279,295,327,112,142,280,296,328,113,277,139,297,325,110,278,140,298,326,108,276,138,299,324,109,667,665,677,663,343,175,46,367,379,368,176,344,47,380,342,174,45,366,378,178,346,42,370,382,179,347,43,371,383,177,345,44,369,381,341,37,173,365,377,339,38,171,363,375,340,36,172,364,376,40,337,169,361,373,41,338,170,362,374,39,336,168,360,372,670,672,668,678,307,129,69,255,403,256,130,308,70,404,306,131,71,257,402,128,310,68,254,406,126,311,66,252,407,127,309,67,253,405,305,60,120,261,401,303,61,121,262,399,304,62,122,263,400,63,301,123,260,397,64,302,124,258,398,65,300,125,259,396,682,676,664,680 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#fd865ad85ec1badfd7a7711949755519f1db0e961ea1bdb330ad04fd991385b2, 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 21:55:50 · history