Equation 677 Database

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Magma 7c6fc8d788c4…

magma 7c6fc8d788c4
Size
705
Isomorphism class hash
7c6fc8d788c477f18287b1ed734532104e54ec9fff028594364937bc0060aa43
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 21:46:46
Display reorder
660,43,464,465,471,468,44,430,431,426,423,42,444,445,452,449,524,46,525,533,529,484,485,493,489,47,504,45,505,513,509,41,585,584,593,589,39,545,544,553,549,40,565,564,573,569,645,37,644,653,649,613,605,38,604,609,625,36,624,633,629,691,687,694,696,226,462,470,467,469,227,420,425,422,424,225,442,451,448,450,523,222,532,528,530,483,492,488,490,223,503,224,512,508,510,217,592,583,588,590,218,552,543,548,550,216,572,563,568,570,652,220,643,648,650,608,612,221,603,610,632,219,623,628,630,685,688,690,686,0,19,259,62,93,2,20,260,60,94,1,18,258,61,95,22,4,262,65,92,23,263,63,90,5,21,3,261,64,91,7,257,17,68,84,8,255,15,66,85,6,256,16,67,86,253,10,13,71,87,69,254,11,14,88,252,9,12,70,89,670,672,681,666,118,290,410,386,130,119,288,408,384,131,117,289,409,385,129,293,114,413,389,126,291,411,387,127,115,292,116,412,388,128,109,416,296,392,121,110,414,294,390,122,108,415,295,391,120,419,112,299,395,124,393,417,113,297,125,418,111,298,394,123,678,676,683,664,210,460,461,473,474,211,429,428,433,434,212,441,440,456,457,521,213,522,536,537,481,482,496,497,214,501,215,502,516,517,208,581,582,596,597,209,540,542,556,557,207,561,562,576,577,640,204,642,656,657,616,601,205,602,617,620,206,622,636,637,695,697,703,701,48,477,478,476,479,49,438,439,437,436,50,446,458,455,454,526,51,538,531,535,486,498,491,495,52,506,53,518,511,515,54,598,586,591,595,55,558,546,551,555,56,578,566,571,575,658,57,646,651,655,611,618,58,606,615,638,59,626,631,635,689,702,699,700,34,472,463,466,475,35,427,421,432,435,33,453,443,447,459,534,30,520,527,539,494,480,487,499,31,514,32,500,507,519,25,580,594,587,599,26,541,554,547,559,24,560,574,567,579,641,28,654,647,659,607,600,29,614,619,621,27,634,627,639,693,698,704,692,240,314,326,231,350,241,312,324,232,348,242,313,325,233,349,317,243,329,230,353,315,327,228,351,244,316,245,328,229,352,246,332,320,237,356,247,330,318,238,354,248,331,319,239,355,335,249,323,236,359,234,333,250,321,357,334,251,322,235,358,679,673,668,667,132,188,105,374,302,133,186,106,372,300,134,187,107,373,301,191,135,104,377,305,189,102,375,303,136,190,137,103,376,304,138,96,183,380,308,139,97,184,378,306,140,98,185,379,307,99,141,182,383,311,381,100,142,180,309,101,143,181,382,310,677,665,675,684,82,266,338,362,398,83,264,336,360,396,81,265,337,361,397,269,78,341,365,401,267,339,363,399,79,268,80,340,364,400,73,344,272,368,404,74,342,270,366,402,72,343,271,367,403,347,76,275,371,407,369,345,77,273,405,346,75,274,370,406,674,680,671,661,196,152,165,278,172,197,150,166,276,173,195,151,167,277,171,155,192,164,281,168,153,162,279,169,193,154,194,163,280,170,202,156,147,284,178,203,157,148,282,179,201,158,149,283,177,159,198,146,287,174,285,160,199,144,175,161,200,145,286,176,663,662,669,682 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#f4f724834d898f30c0a6fbb58eb0b496232f556dc00d71550d6e526db5e670b8, 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 21:46:46 · history