Equation 677 Database

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Magma d1edd5fe80e4…

magma d1edd5fe80e4
Size
705
Isomorphism class hash
d1edd5fe80e4015e2e6b443d546efd07d59ffa0d22eb33d960ce02f17c0f4b49
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 21:09:12
Display reorder
704,458,469,510,498,456,470,511,499,457,468,512,500,461,513,472,501,459,473,502,514,460,515,471,503,496,464,475,508,497,462,476,509,463,495,474,507,492,467,478,504,493,465,479,505,494,466,477,506,487,488,486,490,491,489,485,483,480,481,482,484,701,700,702,703,656,657,659,658,648,649,651,650,652,653,655,654,640,643,641,642,645,644,646,647,636,639,637,638,622,620,621,623,614,612,613,615,616,618,617,619,634,633,632,635,626,625,624,627,630,629,628,631,2,1,0,5,3,4,8,6,10,11,9,7,689,691,688,690,257,267,42,245,255,268,43,243,256,269,44,244,253,45,266,241,254,264,242,46,252,47,265,240,251,263,273,40,249,261,274,41,262,250,275,39,247,259,272,36,248,260,270,37,246,258,271,38,231,232,233,230,228,229,237,238,235,236,234,239,672,675,673,674,165,179,82,153,166,177,83,154,167,178,81,155,164,78,175,152,162,176,150,79,163,80,174,151,144,156,170,73,145,157,168,74,158,146,169,72,147,159,173,76,148,160,171,77,149,161,172,75,142,143,141,138,139,140,133,134,135,136,137,132,683,681,682,680,333,346,23,369,334,347,21,370,335,345,22,371,332,19,342,368,330,343,366,20,331,18,344,367,360,324,337,14,361,325,338,12,326,362,336,13,363,327,340,17,364,328,341,15,365,329,339,16,358,359,357,354,355,356,349,350,351,352,353,348,692,693,695,694,111,122,48,101,112,120,49,99,113,121,50,100,110,51,125,97,108,123,98,52,109,53,124,96,107,117,128,54,105,118,126,55,119,106,127,56,103,116,131,57,104,114,129,58,102,115,130,59,87,88,89,86,84,85,93,94,91,92,90,95,697,698,696,699,538,550,450,526,539,551,451,527,537,549,452,525,534,453,546,522,535,547,523,454,536,455,548,524,517,529,541,448,518,530,542,449,528,516,540,447,520,532,544,444,521,533,545,445,519,531,543,446,561,562,563,560,558,559,552,553,557,555,556,554,684,686,685,687,296,308,35,284,294,306,33,282,295,307,34,283,299,31,311,287,297,309,285,32,298,30,310,286,279,291,303,26,280,292,304,24,293,281,305,25,278,290,302,29,276,288,300,27,277,289,301,28,318,319,320,321,322,323,316,317,314,312,313,315,663,661,662,660,205,222,68,195,206,223,66,196,204,224,67,197,208,71,225,194,209,226,192,69,207,70,227,193,201,211,220,63,202,212,221,64,210,203,219,65,200,214,216,62,198,215,217,60,199,213,218,61,183,184,185,182,180,181,189,190,187,188,186,191,678,676,679,677,373,391,420,412,374,392,421,413,372,390,422,411,376,423,394,408,377,395,409,424,375,425,393,410,418,379,389,426,419,380,387,427,378,417,388,428,414,382,385,429,415,383,386,430,416,381,384,431,401,399,400,397,398,396,407,405,402,403,404,406,667,665,666,664,604,570,440,595,605,571,438,596,603,572,439,594,600,443,573,598,601,574,599,441,602,442,575,597,593,610,568,435,591,611,569,436,609,592,567,437,589,606,564,434,590,607,565,432,588,608,566,433,582,583,584,585,586,587,580,581,578,576,577,579,671,670,668,669 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#d999f02d519da9e6482c93589338b3231f65cc1ce6e36c19968e5d782b765397, 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 21:09:13 · history