Equation 677 Database

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Magma 15f8c6ebcb5d…

magma 15f8c6ebcb5d
Size
705
Isomorphism class hash
15f8c6ebcb5df685b7f511b0e5c2dbb2607f2a84065f54c45ef28a3ed8dd9ec9
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 19:20:51
Display reorder
660,13,216,383,44,157,14,217,42,384,158,43,218,12,385,156,219,16,382,47,160,220,17,380,45,161,221,15,381,46,159,19,222,389,39,163,20,223,390,40,164,18,224,391,41,162,22,225,388,38,166,23,226,386,36,167,21,227,387,37,165,662,665,663,667,103,122,320,50,417,104,120,48,318,418,49,121,102,319,419,125,106,323,53,416,123,107,321,51,414,124,105,322,52,415,101,128,315,56,423,99,126,316,54,424,100,127,317,55,425,97,131,314,59,422,98,129,312,57,420,96,130,313,58,421,686,691,685,688,269,181,279,257,245,267,182,255,280,243,256,180,268,281,244,184,265,278,253,241,185,266,276,254,242,183,264,277,252,240,275,187,285,263,251,273,188,286,261,249,274,186,287,262,250,271,190,284,259,247,272,191,282,260,248,270,189,283,258,246,668,669,671,670,33,65,523,441,559,34,63,442,524,560,443,64,35,525,561,61,32,522,440,558,62,30,520,438,556,60,31,521,439,557,24,71,529,447,565,25,69,530,448,566,26,70,531,449,567,27,67,528,446,564,28,68,526,444,562,29,66,527,445,563,678,674,676,673,499,82,334,535,339,500,83,536,335,340,537,81,501,333,341,78,498,330,534,338,79,496,331,532,336,80,497,332,533,337,505,73,325,541,345,506,74,326,542,346,507,72,324,543,347,504,76,328,540,344,502,77,329,538,342,503,75,327,539,343,661,666,672,664,583,173,429,631,233,584,171,632,430,231,633,172,585,431,232,169,582,428,630,229,170,580,426,628,230,168,581,427,629,228,589,179,435,637,239,590,177,436,638,237,591,178,437,639,238,588,175,434,636,235,586,176,432,634,236,587,174,433,635,234,693,700,695,698,404,0,368,489,373,405,2,490,369,374,491,4,406,367,375,6,407,364,488,372,8,408,365,486,370,11,409,366,487,371,410,10,360,495,379,655,7,653,654,652,658,9,657,659,656,411,3,362,494,378,412,5,363,492,376,413,1,361,493,377,702,704,701,703,477,84,395,607,453,478,85,608,396,454,609,86,479,397,455,87,476,394,606,452,88,474,392,604,450,89,475,393,605,451,483,90,401,613,459,484,91,402,614,460,485,92,403,615,461,482,93,400,612,458,480,94,398,610,456,481,95,399,611,457,696,699,694,697,215,154,595,306,571,213,155,307,596,572,308,153,214,597,573,150,211,594,309,570,151,212,592,310,568,152,210,593,311,569,206,145,601,304,577,204,146,602,305,578,205,144,603,303,579,209,148,600,300,576,207,149,598,301,574,208,147,599,302,575,679,682,681,684,547,108,134,643,511,548,109,644,132,512,645,110,549,133,513,111,546,137,642,510,112,544,135,640,508,113,545,136,641,509,553,114,140,649,517,554,115,138,650,518,555,116,139,651,519,552,117,143,648,516,550,118,141,646,514,551,119,142,647,515,675,683,680,677,465,201,619,355,288,466,202,356,620,289,354,203,467,621,290,200,464,618,358,291,198,462,616,359,292,199,463,617,357,293,471,192,625,353,294,472,193,626,351,295,473,194,627,352,296,470,195,624,349,297,468,196,622,350,298,469,197,623,348,299,692,689,690,687 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#9f23da9903d6ebc1c6f98cbe23264669be86f8e7144737b42fbccbf8aeddcd62, 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 19:20:51 · history