Equation 677 Database

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Magma 8aced4aebfdd…

magma 8aced4aebfdd
Size
705
Isomorphism class hash
8aced4aebfdd73d95851159fb319e851fad83f499e099f6b14bda52b1448f453
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 17:19:52
Display reorder
660,552,419,290,384,432,550,420,291,382,430,551,418,289,383,431,548,415,293,380,428,294,416,549,381,429,417,547,292,379,427,543,410,296,375,423,541,411,297,373,421,542,409,295,374,422,413,546,299,378,426,414,544,300,376,424,412,545,298,377,425,675,677,674,685,264,199,30,245,396,262,200,31,246,394,263,201,29,244,395,260,202,26,241,392,27,203,261,242,393,204,259,28,243,391,255,197,21,251,387,253,198,22,252,385,254,196,20,250,386,193,258,24,247,390,194,256,25,248,388,195,257,23,249,389,670,663,667,662,579,480,54,66,159,577,478,55,67,157,578,479,53,65,158,575,476,50,62,162,51,477,576,63,160,475,574,52,64,161,570,471,45,57,165,568,469,46,58,163,569,470,44,56,164,474,573,48,60,168,472,571,49,61,166,473,572,47,59,167,683,687,679,686,655,657,78,654,652,639,641,79,638,637,647,649,77,646,644,623,625,74,622,621,75,633,631,630,629,617,615,76,614,613,140,555,69,133,132,138,553,70,134,130,139,554,68,135,131,606,604,72,609,608,556,141,73,136,129,557,142,71,137,128,703,697,699,704,92,285,305,516,492,93,283,306,514,490,94,284,304,515,491,95,288,301,512,488,302,286,96,513,489,287,97,303,511,487,98,280,311,507,483,99,281,312,505,481,100,282,310,506,482,279,101,307,510,486,277,102,308,508,484,278,103,309,509,485,693,692,694,689,456,327,173,591,528,454,325,174,589,526,455,326,172,590,527,452,330,169,587,524,170,328,453,588,525,329,451,171,586,523,447,333,179,582,519,445,331,180,580,517,446,332,178,581,518,336,450,175,585,522,334,448,176,583,520,335,449,177,584,521,672,668,661,664,37,213,186,111,218,35,211,184,112,219,36,212,185,110,217,33,216,182,114,221,183,214,34,115,222,215,32,181,113,220,43,208,192,109,224,41,209,190,107,225,42,210,191,108,223,207,39,188,105,227,205,40,189,106,228,206,38,187,104,226,691,695,696,690,444,468,127,540,603,442,466,125,538,601,443,467,126,539,602,440,464,123,536,599,124,465,441,537,600,463,439,122,535,598,435,459,118,531,594,433,457,116,529,592,434,458,117,530,593,462,438,121,534,597,460,436,119,532,595,461,437,120,533,596,684,688,678,682,653,658,233,656,659,636,642,234,640,643,645,650,232,648,651,620,626,229,624,627,230,634,628,632,635,618,612,231,616,619,15,560,239,18,565,16,558,240,19,563,14,559,238,17,564,611,610,235,605,607,561,12,236,143,566,562,13,237,144,567,702,701,700,698,6,272,145,504,88,7,273,146,502,86,8,271,147,503,87,9,275,148,500,91,149,276,10,501,89,274,11,150,499,90,4,270,151,495,83,5,268,152,493,84,3,269,153,494,85,266,1,154,498,82,267,0,155,496,80,265,2,156,497,81,666,669,671,665,337,353,320,408,372,338,354,321,406,370,339,352,319,407,371,340,349,323,404,368,324,350,341,405,369,351,342,322,403,367,343,359,318,399,363,344,360,316,397,361,345,358,317,398,362,355,346,314,402,366,356,347,315,400,364,357,348,313,401,365,676,673,680,681 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#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 17:19:53 · history