Equation 677 Database

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Magma 8e11f75e5276…

magma 8e11f75e5276
Size
705
Isomorphism class hash
8e11f75e527600e8cbe7f5985494b9c3010d7080729025a7e951cf9c048308c1
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 19:53:55
Display reorder
660,416,464,488,206,389,414,462,387,486,204,415,463,388,487,205,419,467,385,491,209,417,465,386,489,207,418,466,384,490,208,422,470,380,494,212,420,468,378,492,210,493,421,469,379,211,473,425,383,497,215,471,423,381,495,213,472,424,382,496,214,665,662,664,663,299,310,287,276,152,297,311,150,285,277,298,309,151,286,278,295,306,155,283,279,296,307,153,284,280,294,308,154,282,281,305,316,147,293,274,303,317,148,291,275,292,304,315,149,273,312,301,146,289,270,313,302,144,290,271,314,300,145,288,272,686,687,691,688,341,352,327,170,232,339,353,233,328,168,340,351,231,329,169,337,348,228,326,173,338,349,229,324,171,336,350,230,325,172,332,343,238,318,176,330,344,239,319,174,320,331,342,237,175,346,335,234,321,179,347,333,235,322,177,345,334,236,323,178,672,667,666,661,452,404,500,102,127,450,402,128,498,103,451,403,126,499,104,455,407,130,503,105,453,405,131,501,106,454,406,129,502,107,458,410,125,506,100,456,408,123,504,101,505,457,409,124,99,413,461,121,509,96,411,459,122,507,97,412,460,120,508,98,680,679,674,677,37,58,138,264,119,38,59,117,139,265,36,57,118,140,266,40,54,115,141,267,41,55,116,142,268,39,56,114,143,269,43,49,110,136,262,44,50,108,137,263,135,42,48,109,261,52,46,113,132,258,53,47,111,133,259,51,45,112,134,260,671,668,669,670,392,6,512,602,221,390,4,219,510,600,391,5,220,511,601,395,9,217,515,605,393,10,218,513,603,394,3,216,514,604,398,7,227,518,608,396,8,225,516,606,517,397,11,226,607,2,401,223,521,611,1,399,224,519,609,0,400,222,520,610,695,699,693,694,595,536,254,554,247,596,534,248,252,552,594,535,246,253,553,598,539,250,257,557,599,537,251,255,555,597,538,249,256,556,647,644,245,645,646,639,636,243,637,638,641,643,640,244,642,656,659,241,657,658,648,651,242,649,650,652,655,240,653,654,701,703,702,704,560,94,60,542,14,558,95,12,61,540,559,93,13,62,541,563,90,17,63,545,561,91,15,64,543,562,92,16,65,544,566,85,20,66,548,564,86,18,67,546,68,565,84,19,547,88,569,23,69,551,89,567,21,70,549,87,568,22,71,550,698,696,700,697,376,524,428,192,77,377,522,75,426,193,375,523,76,427,194,372,527,73,431,195,373,525,74,429,196,374,526,72,430,197,367,530,83,434,198,368,528,81,432,199,433,366,529,82,200,533,370,79,437,201,531,371,80,435,202,532,369,78,436,203,675,673,681,684,440,476,572,626,28,438,474,29,570,624,439,475,27,571,625,443,479,24,575,629,441,477,25,573,627,442,478,26,574,628,446,482,34,578,632,444,480,35,576,630,577,445,481,33,631,485,449,30,581,635,483,447,31,579,633,484,448,32,580,634,682,683,678,676,189,362,614,584,160,190,360,161,612,582,191,361,159,613,583,188,365,156,617,587,186,363,157,615,585,187,364,158,616,586,180,357,166,620,590,181,358,167,618,588,619,182,359,165,589,356,183,162,623,593,354,184,163,621,591,355,185,164,622,592,692,689,690,685 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#b307f9e79abd0b0dc3c5454ee1dbc0a12bcd3b395b4c4aa55143605b1deda3bc, 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 19:53:56 · history