Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 91a75eb2761d…

magma 91a75eb2761d
Size
705
Isomorphism class hash
91a75eb2761d9b5881432f31d68d4a811fc894ba8fd31e2239b8b71ec44ca6af
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 19:47:56
Display reorder
660,89,610,613,608,615,87,630,633,628,635,653,88,648,655,650,590,85,593,588,595,550,553,86,548,555,570,84,573,568,575,95,431,429,427,433,93,453,450,448,455,94,473,470,468,475,493,91,490,488,495,513,92,510,508,515,533,90,530,528,535,685,691,697,688,52,602,617,614,611,53,622,637,634,631,657,51,654,651,642,582,48,597,594,591,542,557,49,554,551,562,50,577,574,571,58,435,424,432,430,59,457,441,454,451,57,477,461,474,471,497,54,480,494,491,517,55,501,514,511,537,56,521,534,531,698,694,703,686,41,417,345,321,369,39,418,346,322,370,347,40,323,371,419,416,37,344,320,368,414,342,38,318,366,415,36,343,319,367,47,336,408,312,360,45,337,409,313,361,46,338,410,314,362,339,43,411,315,363,340,44,412,316,364,341,42,413,317,365,664,671,669,681,164,393,14,209,405,162,394,12,207,406,13,163,208,407,395,392,167,17,205,404,390,15,165,206,402,391,166,16,204,403,159,20,384,215,396,160,18,385,213,397,161,19,386,214,398,23,158,387,211,399,21,156,388,212,400,22,157,389,210,401,673,678,667,675,67,603,619,616,609,68,623,639,636,629,659,66,656,649,643,583,70,599,596,589,543,559,71,556,549,563,69,579,576,569,65,439,425,434,428,63,459,443,456,449,64,479,463,476,469,499,61,483,496,489,519,62,503,516,509,539,60,523,536,529,701,687,690,689,4,612,606,605,607,5,632,626,625,627,646,3,645,647,652,592,1,586,585,587,552,546,0,545,547,572,2,566,565,567,10,438,422,420,421,11,446,452,445,447,9,466,472,465,467,486,6,492,485,487,506,7,512,505,507,526,8,532,525,527,696,695,699,693,33,604,600,618,601,34,624,621,638,620,641,35,658,640,644,584,32,580,598,581,544,541,30,558,540,564,31,560,578,561,24,437,426,436,423,25,440,444,458,442,26,460,464,478,462,481,27,484,498,482,500,28,504,518,502,520,29,524,538,522,704,702,700,692,196,287,297,275,263,197,285,298,273,261,299,195,274,262,286,283,192,296,271,259,284,294,193,272,260,282,194,295,270,258,202,288,278,266,254,203,289,276,264,252,201,290,277,265,253,291,198,281,269,257,292,199,279,267,255,293,200,280,268,256,661,676,663,679,220,381,232,176,73,221,382,233,174,74,231,219,175,72,383,380,216,228,179,76,378,229,217,177,77,379,218,230,178,75,226,238,372,171,79,227,239,373,172,80,225,237,374,173,78,234,222,375,170,82,235,223,376,168,83,236,224,377,169,81,662,683,665,674,300,106,118,148,357,301,107,119,149,358,117,302,147,359,105,102,303,114,144,356,103,115,304,145,354,104,305,116,146,355,306,109,97,154,348,307,110,98,155,349,308,108,96,153,350,112,309,100,150,351,113,310,101,151,352,111,311,99,152,353,668,670,684,682,127,250,191,333,143,128,251,189,334,141,190,126,335,142,249,246,130,187,332,139,247,188,131,330,140,248,129,186,331,138,125,182,241,324,134,123,180,242,325,132,124,181,240,326,133,185,121,244,327,137,183,122,245,328,135,184,120,243,329,136,666,677,672,680 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#aa12d1af20c50a7f712e8df2ac0f984d22557fb7db3e49cc75c20296525d3597, 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 19:47:57 · history