Equation 677 Database

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Magma ec8479018c57…

magma ec8479018c57
Size
705
Isomorphism class hash
ec8479018c5746810d72997fbc881d37e00811b3a87b651796ecbd79c881df85
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 19:57:17
Display reorder
660,151,308,545,294,367,546,152,295,368,306,544,153,307,296,366,541,150,304,293,363,305,148,542,291,364,543,149,303,292,365,299,536,285,157,358,297,537,286,158,359,298,535,287,159,357,539,302,288,156,361,540,300,289,154,362,155,538,301,290,360,669,661,667,665,277,223,47,461,403,48,278,462,404,224,49,276,225,460,402,50,273,222,457,399,220,274,51,458,400,52,275,221,459,401,229,45,452,283,394,230,46,453,284,395,231,44,451,282,393,41,228,455,279,397,42,226,456,280,398,281,43,227,454,396,688,687,685,690,332,604,92,121,557,93,330,122,558,605,94,331,603,123,556,91,328,600,120,553,601,329,89,118,554,90,327,602,119,555,595,98,112,323,548,596,99,113,321,549,594,100,114,322,547,97,598,115,326,551,95,599,116,324,552,325,96,597,117,550,671,668,662,670,237,509,181,379,193,182,235,380,194,510,183,236,508,378,195,180,233,505,375,192,506,234,178,376,190,179,232,507,377,191,500,172,370,243,184,501,173,371,241,185,499,174,369,242,186,175,503,373,239,187,176,504,374,240,188,238,177,502,372,189,674,677,680,678,58,9,497,415,628,498,56,416,629,10,496,57,8,414,627,493,54,5,411,624,6,55,494,412,625,495,53,7,413,626,15,488,406,64,619,16,489,407,62,620,14,487,405,63,618,491,11,409,60,622,492,12,410,61,623,59,490,13,408,621,663,672,664,666,164,616,485,310,580,486,165,311,581,617,484,163,615,309,579,481,160,612,313,576,613,161,482,314,577,483,162,614,312,578,607,476,316,170,571,608,477,317,171,572,606,475,315,169,570,479,610,319,166,574,480,611,320,167,575,168,478,609,318,573,693,695,694,698,79,101,417,569,438,658,77,659,656,657,418,78,108,568,437,420,82,110,565,434,111,80,421,566,435,419,81,109,567,436,107,423,560,85,429,105,424,561,83,430,106,422,559,84,428,426,103,563,88,432,427,104,564,86,433,87,425,102,562,431,704,702,703,701,202,253,653,652,24,654,203,655,25,254,651,204,255,650,23,645,205,252,644,27,250,206,647,646,28,648,207,251,649,26,244,257,0,200,22,245,258,2,201,20,246,256,1,199,21,260,247,4,196,18,643,248,642,197,19,198,259,249,3,17,700,697,699,696,146,473,521,356,640,522,147,354,641,474,520,145,472,355,639,517,142,469,352,636,470,143,518,353,637,519,144,471,351,638,464,512,347,137,631,465,513,345,138,632,463,511,346,136,630,515,467,350,140,634,516,468,348,141,635,139,514,466,349,633,673,684,679,676,215,268,40,592,449,38,216,593,450,269,39,214,267,591,448,36,218,271,588,445,272,219,37,589,446,35,217,270,590,447,266,31,583,213,440,264,29,584,211,441,265,30,582,212,439,34,262,586,209,443,32,263,587,210,444,208,33,261,585,442,681,675,682,683,67,134,533,391,341,534,65,392,339,135,532,66,133,390,340,529,70,130,387,344,131,68,530,388,342,531,69,132,389,343,125,524,382,73,336,126,525,383,71,337,124,523,381,72,338,527,128,385,76,335,528,129,386,74,333,75,526,127,384,334,686,691,689,692 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#b7ef46c52e3181531ee451cc516c519f12d29148a838b2a4381cb7ae279fb33d, 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 19:57:18 · history