Equation 677 Database

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Magma f2cd230a3de5…

magma f2cd230a3de5
Size
705
Isomorphism class hash
f2cd230a3de5053258065cfab8ece149e47cd1b4a589c978ad8739bd77b08cec
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 17:38:28
Display reorder
660,123,350,318,322,345,343,351,124,316,323,349,344,125,317,324,341,122,346,321,325,120,342,347,319,326,340,121,348,320,327,313,336,129,356,328,334,130,357,314,329,335,131,355,315,330,128,339,352,312,331,126,337,353,310,332,127,338,354,311,333,669,672,668,661,281,222,589,541,624,625,220,282,590,542,221,623,280,588,540,620,284,225,585,537,285,621,223,586,538,622,283,224,587,539,595,630,279,217,547,631,277,218,596,548,629,278,219,594,546,275,626,216,591,543,276,627,214,592,544,274,628,215,593,545,690,686,691,685,155,470,79,601,434,435,471,153,80,602,469,433,154,78,600,430,151,466,82,597,152,431,467,83,598,432,150,468,81,599,77,440,146,476,607,441,144,477,75,608,439,145,475,76,606,149,436,472,73,603,147,437,473,74,604,148,438,474,72,605,665,670,663,664,213,482,422,235,458,459,483,211,423,236,481,457,212,421,237,454,209,478,418,234,210,455,479,419,232,456,208,480,420,233,428,464,204,488,226,465,202,489,429,227,463,203,487,427,228,207,460,484,424,229,205,461,485,425,230,206,462,486,426,231,675,682,677,679,246,636,553,365,371,372,637,244,554,366,635,370,245,552,364,374,249,632,549,368,247,375,633,550,369,373,248,634,551,367,559,377,241,642,363,378,242,643,560,361,376,243,641,558,362,240,380,638,555,359,238,381,639,556,360,239,379,640,557,358,667,662,666,671,139,49,43,577,494,495,50,140,44,578,48,493,138,42,576,490,142,52,46,573,143,491,53,47,574,492,141,51,45,575,41,500,137,55,583,501,135,56,39,584,499,136,54,40,582,133,496,58,37,579,134,497,59,38,580,132,498,57,36,581,693,699,695,694,70,530,613,193,186,187,531,71,614,194,529,185,69,612,192,189,66,526,609,196,67,190,527,610,197,188,68,528,611,195,619,184,61,536,191,659,62,656,658,657,183,60,535,618,198,64,180,532,615,199,65,181,533,616,200,63,182,534,617,201,704,703,702,701,7,259,389,395,518,519,260,8,390,396,261,517,6,388,394,514,3,258,392,398,4,515,256,393,399,516,5,257,391,397,387,524,0,250,401,525,2,251,385,402,523,1,252,386,400,32,520,253,383,404,35,521,254,384,405,31,522,255,382,403,700,697,696,698,299,169,506,108,446,447,170,300,507,109,168,445,298,505,110,442,302,172,502,111,303,443,173,503,112,444,301,171,504,113,512,452,305,175,114,453,306,176,513,115,451,304,174,511,116,308,448,178,508,117,309,449,179,509,118,307,450,177,510,119,680,678,676,684,263,565,410,648,11,9,566,264,411,649,564,10,262,409,647,14,266,561,406,644,267,12,562,407,645,13,265,563,408,646,416,17,269,571,654,15,270,572,417,655,16,268,570,415,653,272,20,567,412,650,273,18,568,413,651,271,19,569,414,652,674,683,673,681,33,105,294,164,85,86,106,34,292,162,107,84,27,293,163,88,29,104,297,167,30,89,102,295,165,87,28,103,296,166,289,91,26,96,159,92,24,97,290,160,90,25,98,291,161,22,94,99,288,158,23,95,100,286,156,21,93,101,287,157,689,688,687,692 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#5b838974e03a318bd69da9937fbfbee1bd56d732e0aad8a944a467873e322378, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 17:38:29 · history