Equation 677 Database

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Magma dd01e65b55f3…

magma dd01e65b55f3
Size
705
Isomorphism class hash
dd01e65b55f3dc3ad95162b610b95f2f6f08055c6a861a94aff6e9546328cdc4
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 17:38:52
Display reorder
660,454,447,449,448,241,474,467,242,469,468,425,423,240,431,430,517,509,244,511,510,537,529,245,531,530,497,489,243,491,490,571,577,569,247,570,597,589,248,591,590,557,549,246,551,550,629,637,250,631,630,649,657,251,651,650,609,617,249,611,610,690,686,688,697,451,440,453,441,56,471,460,54,473,461,424,420,55,434,426,514,500,59,516,502,534,520,57,536,522,494,481,58,496,482,576,574,562,51,563,594,582,52,596,583,554,542,53,556,543,622,634,50,636,623,642,654,48,656,643,602,614,49,616,603,695,702,701,693,313,373,337,361,216,314,374,217,338,362,312,372,218,336,360,316,376,219,340,364,317,377,220,341,365,315,375,221,339,363,343,319,379,222,367,320,380,223,344,368,318,378,224,342,366,382,322,225,346,370,383,323,226,347,371,381,321,227,345,369,669,674,675,663,109,385,302,75,179,110,386,177,300,76,108,384,178,301,77,112,388,175,305,74,113,389,176,303,72,111,387,174,304,73,308,115,391,170,81,116,392,168,306,82,114,390,169,307,83,394,118,173,311,80,395,119,171,309,78,393,117,172,310,79,665,677,679,670,442,443,459,458,45,462,463,46,479,478,427,428,47,438,436,501,503,44,518,512,521,523,42,538,532,480,483,43,498,492,578,561,564,36,572,581,584,37,598,592,540,544,38,558,552,624,620,39,638,632,644,641,40,658,652,604,600,41,618,612,699,685,696,689,457,456,452,450,285,476,477,286,472,470,439,437,287,433,432,504,505,284,515,513,524,525,282,535,533,484,485,283,495,493,575,565,560,276,573,585,580,277,595,593,545,541,278,555,553,621,625,279,635,633,640,645,280,655,653,601,605,281,615,613,691,687,698,692,455,446,445,444,34,475,466,35,465,464,435,429,33,422,421,519,508,30,507,506,539,528,31,527,526,499,488,32,487,486,567,579,568,25,566,599,588,26,587,586,559,548,24,547,546,628,639,28,627,626,648,659,29,647,646,608,619,27,607,606,703,704,694,700,135,153,122,289,6,136,154,7,120,290,137,155,8,121,288,134,152,9,125,292,132,150,10,123,293,133,151,11,124,291,128,141,144,4,295,142,145,5,126,296,143,146,3,127,294,147,140,1,131,298,148,138,0,129,299,149,139,2,130,297,682,661,662,681,272,258,105,237,95,270,259,93,106,238,271,260,94,107,239,275,261,91,104,236,273,262,92,102,234,274,263,90,103,235,96,267,256,86,228,268,257,84,97,229,269,255,85,98,230,252,266,89,99,231,253,264,87,100,232,254,265,88,101,233,676,668,673,678,202,205,183,349,162,203,206,163,184,350,201,204,164,185,348,198,208,165,182,352,199,209,166,180,353,200,207,167,181,351,189,193,211,160,355,194,212,161,190,356,192,210,159,191,354,214,196,156,188,358,215,197,157,186,359,213,195,158,187,357,666,672,680,671,398,399,23,325,69,400,401,70,21,326,396,397,71,22,324,404,405,68,19,328,406,407,66,20,329,403,402,67,18,327,14,411,410,60,331,413,412,61,12,332,409,408,62,13,330,416,417,63,17,334,418,419,64,15,335,414,415,65,16,333,667,664,684,683 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#5c1fa523b4d9d2fbb415708ccaff34546079d57eeb66e712dcba93d7172179c8, 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 17:38:53 · history