Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma e5a16ab59531…

magma e5a16ab59531
Size
705
Isomorphism class hash
e5a16ab5953142a57ec0dcc7a0d518961a3ae3b9b3869c3c1f3e07e52091a23c
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 17:41:51
Display reorder
660,337,151,349,324,313,338,314,152,350,325,336,312,150,348,326,147,333,309,345,323,148,334,310,346,321,149,335,311,347,322,340,157,328,304,315,158,329,305,341,316,156,327,303,339,317,331,153,307,343,318,332,154,308,344,319,330,155,306,342,320,685,686,688,687,449,49,412,437,425,447,423,50,413,435,448,424,48,411,436,52,452,428,415,440,53,450,426,416,438,51,451,427,414,439,418,55,455,431,443,56,453,429,419,441,54,454,430,417,442,458,58,434,421,446,456,59,432,422,444,457,57,433,420,445,701,702,704,703,574,297,585,561,551,575,549,298,586,562,573,550,299,587,563,300,570,547,584,560,301,571,548,582,558,302,572,546,583,559,576,295,565,542,552,296,566,540,577,553,294,564,541,578,554,568,291,545,579,555,569,292,543,580,556,567,293,544,581,557,670,669,672,671,43,61,467,113,212,44,210,62,465,111,42,211,60,466,112,64,46,208,470,116,65,47,209,468,114,63,45,207,469,115,462,67,41,218,119,68,39,216,463,117,66,40,217,464,118,37,70,214,461,122,38,71,215,459,120,36,69,213,460,121,680,677,679,678,240,131,78,230,478,241,479,129,79,228,242,477,130,80,229,134,239,481,81,226,132,237,482,82,227,133,238,480,83,225,76,126,231,476,221,127,232,474,77,219,128,233,475,75,220,234,125,472,72,224,235,123,473,73,222,236,124,471,74,223,689,690,691,692,257,188,268,527,144,255,145,186,269,525,256,146,187,267,526,184,260,143,271,530,185,258,141,272,528,183,259,142,270,529,274,194,263,135,522,192,261,136,275,523,193,262,137,273,524,266,190,138,277,521,264,191,139,278,519,265,189,140,276,520,697,698,700,699,635,599,647,623,609,633,610,597,645,621,634,611,598,646,622,595,631,608,643,619,596,632,606,644,620,594,630,607,642,618,638,590,626,600,614,588,624,601,636,612,589,625,602,637,613,629,593,603,641,617,627,591,604,639,615,628,592,605,640,616,661,662,664,663,357,166,21,10,92,358,90,167,22,11,359,91,165,23,9,169,360,95,20,6,170,361,93,18,7,168,362,94,19,8,12,164,355,87,0,162,356,88,13,2,163,354,89,14,1,351,160,86,15,4,352,161,84,16,5,353,159,85,17,3,682,681,684,683,105,201,534,101,282,106,283,202,535,99,107,284,203,536,100,204,108,281,537,97,205,109,279,538,98,206,110,280,539,96,655,199,652,654,653,200,657,658,659,656,198,649,648,650,651,288,195,287,531,103,289,196,285,532,104,290,197,286,533,102,693,694,696,695,490,28,498,245,509,491,507,29,499,243,489,508,27,500,244,24,493,512,497,248,25,494,510,495,246,26,492,511,496,247,504,34,488,515,251,35,486,513,505,249,33,487,514,506,250,484,30,518,503,254,485,31,516,501,252,483,32,517,502,253,666,665,668,667,388,176,399,376,364,389,365,174,400,377,387,363,175,401,375,172,391,367,402,379,173,392,368,403,380,171,390,366,404,378,405,182,394,370,382,180,395,371,406,383,181,393,369,407,381,397,178,373,408,385,398,179,374,409,386,396,177,372,410,384,674,673,676,675 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#6086f0079822f3fde2aa4f203419cd6117656c7d05938f081a69b332c89c02c3, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 17:41:53 · history