Equation 677 Database

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Magma 5e77bf47ded8…

magma 5e77bf47ded8
Size
705
Isomorphism class hash
5e77bf47ded87d8d1347675108bf4a4ee9f69246d9942429a78f531ff9dbf9cd
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 17:19:37
Display reorder
660,645,653,191,650,649,605,613,189,610,609,625,633,190,630,629,565,573,187,570,569,188,593,585,590,589,553,545,186,550,549,465,473,182,470,469,426,433,180,430,429,445,453,181,450,449,533,525,185,530,529,493,485,183,490,489,513,505,184,510,509,689,688,697,703,643,644,147,652,640,603,604,148,612,601,623,624,149,632,620,563,564,146,572,561,144,584,583,592,581,544,543,145,552,540,463,464,153,472,461,424,425,154,432,421,443,444,155,452,441,524,523,152,532,521,484,483,150,492,480,504,503,151,512,501,693,700,691,696,6,371,105,49,287,7,369,106,50,285,8,370,107,48,286,9,367,104,52,283,102,368,10,53,284,366,11,103,51,282,4,362,96,55,278,5,360,97,56,276,3,361,98,54,277,365,1,99,58,281,363,0,100,59,279,364,2,101,57,280,683,663,671,680,218,395,124,311,323,216,393,125,309,321,217,394,123,310,322,221,391,120,307,319,121,392,219,308,320,390,220,122,306,318,224,386,130,302,314,222,384,131,300,312,223,385,129,301,313,389,227,126,305,317,387,225,127,303,315,388,226,128,304,316,664,665,677,672,642,658,16,646,655,602,618,17,606,615,622,638,15,626,635,562,578,12,566,575,13,598,582,586,595,558,542,14,546,555,462,478,22,466,475,423,439,23,437,438,442,458,21,446,455,538,522,18,526,535,498,482,19,486,495,518,502,20,506,515,685,686,704,698,659,657,295,648,651,619,617,296,608,611,639,637,294,628,631,579,577,298,568,571,299,597,599,588,591,557,559,297,548,551,479,477,293,468,471,420,436,291,428,431,459,457,292,448,451,537,539,289,528,531,497,499,290,488,491,517,519,288,508,511,687,702,701,690,654,656,71,641,647,614,616,69,600,607,634,636,70,621,627,574,576,67,560,567,68,596,594,580,587,556,554,66,541,547,474,476,62,460,467,434,435,60,422,427,454,456,61,440,447,536,534,65,520,527,496,494,63,481,487,516,514,64,500,507,695,692,699,694,359,232,138,419,263,357,233,139,417,261,358,231,140,418,262,355,228,141,415,259,142,229,356,416,260,230,354,143,414,258,350,238,136,410,254,348,239,137,408,252,349,237,135,409,253,234,353,132,413,257,235,351,133,411,255,236,352,134,412,256,684,676,670,669,383,335,114,205,200,381,333,115,206,198,382,334,116,204,199,379,331,117,208,203,118,332,380,209,201,330,378,119,207,202,374,326,112,211,195,372,324,113,212,196,373,325,111,210,197,329,377,108,214,194,327,375,109,215,192,328,376,110,213,193,675,681,666,673,347,275,39,172,156,345,273,40,173,157,346,274,41,171,158,343,271,38,168,159,36,272,344,169,160,270,342,37,170,161,338,266,45,178,162,336,264,46,179,163,337,265,47,177,164,269,341,44,174,165,267,339,42,175,166,268,340,43,176,167,662,674,661,668,407,247,35,95,79,405,248,33,93,80,406,246,34,94,78,403,250,31,91,82,32,251,404,92,83,249,402,30,90,81,398,245,26,86,77,396,243,24,84,75,397,244,25,85,76,241,401,29,89,73,242,399,27,87,74,240,400,28,88,72,679,678,667,682 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#4ddcb3732d8cead11c348e4cf9e2318d25466469e5bf7b5d48d8ea06dbb2e5f3, 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 17:19:41 · history