Equation 677 Database

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Magma e732389072f4…

magma e732389072f4
Size
705
Isomorphism class hash
e732389072f47115776f7858afcd4edcbfcf2455afab9ba178ab65972c2bece3
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 19:19:37
Display reorder
660,11,494,488,480,491,9,511,514,508,500,10,531,534,528,520,7,474,471,468,460,8,433,432,430,429,6,454,451,448,447,2,614,611,608,607,1,634,631,628,627,0,654,651,648,647,594,5,591,588,587,554,3,551,548,547,574,4,571,568,567,685,700,693,686,64,490,493,486,495,65,515,510,513,506,63,535,530,533,526,60,470,475,473,466,61,437,439,438,425,62,450,455,453,445,70,610,615,613,605,71,630,635,633,625,69,650,655,653,645,590,66,595,593,585,550,67,555,553,545,570,68,575,573,565,687,690,689,694,183,359,383,407,313,181,314,360,384,408,182,315,361,385,409,179,358,312,382,406,180,356,310,380,404,178,357,311,381,405,189,365,319,389,413,187,366,320,390,414,188,367,321,391,415,364,185,318,388,412,362,186,316,386,410,363,184,317,387,411,673,677,671,665,152,227,301,256,279,153,277,228,302,257,151,278,226,303,258,148,230,275,300,259,149,231,276,298,260,150,229,274,299,261,143,233,285,307,254,144,234,283,308,255,142,232,284,309,253,236,146,281,306,250,237,147,282,304,251,235,145,280,305,252,661,668,663,667,80,496,485,483,492,78,512,516,505,503,79,532,536,525,523,83,476,472,465,463,81,427,426,424,423,82,456,452,444,442,75,616,612,604,602,76,636,632,624,622,77,656,652,644,642,596,74,592,584,582,556,72,552,544,542,576,73,572,564,562,701,702,699,703,271,498,499,487,497,272,517,518,519,507,273,538,537,539,527,270,477,478,479,467,268,421,420,422,428,269,457,458,459,446,262,617,618,619,606,263,638,637,639,626,264,658,657,659,646,597,265,598,599,586,558,266,557,559,546,577,267,578,579,566,697,696,698,695,286,481,484,489,482,287,502,501,504,509,288,522,521,524,529,289,462,461,464,469,290,434,435,436,431,291,440,441,443,449,292,600,601,603,609,293,620,621,623,629,294,640,641,643,649,581,295,580,583,589,540,296,541,543,549,560,297,561,563,569,691,704,688,692,54,43,126,90,139,55,140,44,124,88,56,141,42,125,89,57,46,138,129,93,58,47,136,127,91,59,45,137,128,92,52,41,130,121,84,53,39,131,122,417,51,40,132,123,419,37,48,133,120,87,38,49,134,118,85,36,50,135,119,86,681,678,676,664,245,197,325,20,215,246,216,198,326,18,244,214,196,327,19,248,200,218,324,23,249,201,219,322,21,247,199,217,323,22,243,195,221,331,15,241,193,222,332,16,242,194,220,333,17,191,239,224,330,14,192,240,225,328,12,190,238,223,329,13,666,674,684,680,24,347,172,159,371,25,372,348,173,157,26,373,349,174,158,27,346,370,175,155,28,344,368,176,156,29,345,369,177,154,30,353,377,170,165,31,354,378,171,163,32,355,379,169,164,352,33,376,166,161,350,34,374,167,162,351,35,375,168,160,683,669,670,672,210,334,115,102,395,208,396,335,116,100,209,397,336,117,101,213,337,394,114,105,211,338,392,112,103,212,339,393,113,104,205,340,401,106,97,206,416,402,107,98,207,418,403,108,99,341,204,400,109,96,342,202,398,110,94,343,203,399,111,95,662,682,679,675 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#9dc1b7560e7dd8c4d9175d590a741d2999f3578c3e161e058f60df88b07e0ac9, 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 19:19:38 · history