Equation 677 Database

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Magma e859d69d9a56…

magma e859d69d9a56
Size
705
Isomorphism class hash
e859d69d9a5674b264052bb0d17bdfab55a26ac5ddc397fd85d714fa2dd28112
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 17:44:30
Display reorder
660,124,637,634,631,630,125,656,654,651,650,123,617,614,611,610,557,120,554,551,550,577,121,574,571,570,596,122,594,591,590,130,455,453,451,450,131,477,474,471,470,129,436,434,431,430,516,126,514,511,510,536,127,534,531,530,496,128,494,491,490,691,699,702,700,150,624,636,635,632,151,644,657,655,652,152,604,616,615,612,544,153,556,555,552,564,154,576,575,572,584,155,597,595,592,148,445,456,454,452,149,464,476,475,472,147,424,437,435,432,504,144,517,515,512,524,145,537,535,532,484,146,497,495,492,697,694,696,701,167,298,315,334,382,165,299,316,335,383,166,297,317,333,381,294,163,314,330,378,295,164,312,331,379,296,162,313,332,380,158,289,321,325,373,156,290,322,326,374,157,288,323,324,372,292,161,320,328,376,293,159,318,329,377,291,160,319,327,375,667,674,665,661,182,418,358,106,25,180,419,359,107,26,181,417,357,105,24,414,185,354,102,28,415,183,355,103,29,416,184,356,104,27,188,409,349,97,31,186,410,350,98,32,187,408,348,96,30,412,191,352,100,34,413,189,353,101,35,411,190,351,99,33,676,673,683,670,43,639,625,626,620,44,659,645,646,641,42,619,605,606,600,559,46,545,546,540,579,47,565,566,561,599,45,585,586,581,41,459,446,447,443,39,479,465,466,460,40,439,425,426,421,519,37,505,506,501,539,38,525,526,520,499,36,485,486,481,686,688,685,703,13,623,633,629,622,14,643,653,649,642,12,603,613,609,602,543,16,553,549,542,563,17,573,569,562,583,15,593,589,582,19,458,442,441,440,20,463,473,469,462,18,423,433,429,422,503,22,513,509,502,523,23,533,529,522,483,21,493,489,482,690,695,698,693,80,638,621,628,627,78,658,640,648,647,79,618,601,608,607,558,83,541,548,547,578,81,560,568,567,598,82,580,588,587,75,457,444,449,448,76,478,461,468,467,77,438,420,428,427,518,74,500,508,507,538,72,521,528,527,498,73,480,488,487,689,687,704,692,2,274,370,250,258,1,275,371,251,259,0,273,369,249,260,270,5,366,246,261,271,3,367,247,262,272,4,368,248,263,8,265,361,241,256,6,266,362,242,257,7,264,360,240,255,268,11,364,244,252,269,9,365,245,253,267,10,363,243,254,662,682,663,671,90,286,394,169,112,91,287,395,170,113,92,285,393,168,111,282,93,390,172,108,283,94,391,173,109,284,95,392,171,110,88,277,385,175,118,89,278,386,176,119,87,276,384,174,117,280,84,388,178,114,281,85,389,179,115,279,86,387,177,116,681,669,664,677,200,406,346,142,310,198,407,347,143,311,199,405,345,141,309,402,203,342,138,306,403,201,343,139,307,404,202,344,140,308,195,397,337,133,301,196,398,338,134,302,197,396,336,132,300,400,194,340,136,304,401,192,341,137,305,399,193,339,135,303,684,666,679,668,238,50,61,211,219,239,48,62,212,220,237,49,60,210,221,53,234,64,214,218,51,235,65,215,216,52,236,63,213,217,229,56,67,209,225,230,54,68,207,226,228,55,66,208,227,59,232,70,205,224,57,233,71,206,222,58,231,69,204,223,680,678,675,672 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#61e4460e7132ae46985bdc51b44ba41f1d8967bba1a2e054d2c046422600ec54, 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 17:44:31 · history