Equation 677 Database

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Magma 8d8bbc3c52c3…

magma 8d8bbc3c52c3
Size
705
Isomorphism class hash
8d8bbc3c52c30d1b1bcdd73129d7cfc7d27834937e74511641e104309684f2f9
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 19:13:58
Display reorder
660,132,68,468,48,540,133,69,469,46,541,134,67,467,47,539,71,131,464,44,536,72,129,465,45,537,70,130,466,43,538,138,66,459,39,531,139,64,460,37,532,65,140,458,38,530,62,137,462,42,534,63,135,463,40,535,61,136,461,41,533,679,684,674,681,209,195,241,355,367,210,196,239,353,365,208,197,240,354,366,198,205,244,351,363,199,206,242,352,364,200,207,243,350,362,215,193,236,361,373,216,194,237,359,371,192,214,238,360,372,189,211,235,357,369,190,212,233,358,370,191,213,234,356,368,672,663,669,661,94,322,516,384,420,95,320,517,385,421,96,321,515,383,419,325,93,512,380,416,323,91,513,381,417,324,92,514,382,418,85,317,507,375,411,86,318,508,376,412,319,87,506,374,410,316,88,510,378,414,314,89,511,379,415,315,90,509,377,413,676,678,685,683,649,247,647,646,648,657,245,655,654,656,641,246,639,638,640,250,617,615,614,616,248,625,623,622,624,249,633,631,630,632,299,253,220,202,295,300,251,218,203,296,252,301,219,204,297,256,599,598,601,600,254,609,607,606,608,255,298,217,201,294,697,700,703,704,480,73,348,141,54,481,74,349,142,52,479,75,347,143,53,76,476,344,144,50,77,477,345,145,51,78,478,346,146,49,471,79,339,147,60,472,80,340,148,58,81,470,338,149,59,82,474,342,150,56,83,475,343,151,57,84,473,341,152,55,692,689,691,690,431,107,444,528,335,432,108,445,529,336,433,106,443,527,337,103,430,440,524,334,104,428,441,525,332,105,429,442,526,333,422,98,435,519,326,423,99,436,520,327,97,424,434,518,328,101,425,438,522,329,102,426,439,523,330,100,427,437,521,331,668,670,662,665,168,12,188,593,592,169,10,186,594,595,170,11,187,591,590,8,167,184,1,269,9,165,185,587,586,7,166,183,589,588,174,3,179,281,272,175,0,177,279,270,2,176,178,280,271,6,173,182,277,275,4,171,180,278,273,5,172,181,276,274,696,695,694,693,456,285,584,396,568,457,286,585,397,569,455,287,583,395,567,284,452,580,392,564,282,453,581,393,565,283,454,582,394,566,447,291,575,387,559,448,292,576,388,560,293,446,574,386,558,290,450,578,390,562,288,451,579,391,563,289,449,577,389,561,677,686,680,687,651,112,650,645,644,659,113,658,653,652,643,114,642,637,636,111,619,618,613,612,109,627,626,621,620,110,635,634,628,629,572,118,545,125,123,570,119,543,126,121,120,571,544,124,122,117,603,602,596,597,115,611,610,604,605,116,573,542,127,128,698,702,701,699,504,225,408,18,556,505,226,409,16,557,503,224,407,17,555,221,500,404,14,552,222,501,405,15,553,223,502,406,13,554,495,231,399,24,547,496,232,400,22,548,230,494,398,23,546,227,498,402,20,550,228,499,403,21,551,229,497,401,19,549,666,671,667,664,26,163,492,312,267,27,164,493,313,268,25,162,491,311,266,159,29,488,308,263,160,30,489,309,264,161,28,490,310,265,32,154,483,303,258,33,155,484,304,259,153,31,482,302,257,157,35,486,306,261,158,36,487,307,262,156,34,485,305,260,675,673,688,682 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#954a2425e38b1f8d73f83d01c811c18c22a6cf13713c169e64792ee66a752510, 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 19:13:59 · history