Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma b626a5a72488…

magma b626a5a72488
Size
705
Isomorphism class hash
b626a5a724880348189b68b8b3f1f73217d31457e41c163033c6a9d9f435baa6
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 17:26:27
Display reorder
660,631,637,635,628,107,651,657,105,655,648,611,617,106,615,608,551,557,103,555,548,571,577,104,575,568,591,597,102,595,588,451,453,448,98,446,477,471,96,475,468,437,431,97,435,428,511,517,101,515,508,531,537,99,535,528,491,497,100,495,488,698,703,701,704,636,634,632,620,61,656,654,62,652,640,616,614,60,612,600,556,554,64,552,540,576,574,65,572,560,596,594,63,592,581,449,450,452,67,443,474,476,68,472,460,434,436,66,432,421,516,514,70,512,500,536,534,71,532,520,496,494,69,492,480,691,688,697,700,394,318,370,334,226,395,319,227,371,335,393,320,225,369,333,390,321,222,366,330,391,322,223,367,331,392,323,224,368,332,361,316,385,217,325,317,386,218,362,326,315,384,216,360,324,388,312,220,364,328,389,313,221,365,329,387,314,219,363,327,669,664,672,674,418,255,278,346,249,419,256,250,276,347,417,257,251,277,345,414,254,248,281,342,415,252,246,279,343,416,253,247,280,344,284,261,409,240,337,262,410,241,282,338,263,408,242,283,336,412,260,243,287,340,413,258,244,285,341,411,259,245,286,339,661,665,677,682,621,638,639,629,11,641,658,9,659,649,601,618,10,619,609,541,558,7,559,549,561,579,8,578,569,580,598,6,599,589,458,459,442,2,447,479,461,1,478,469,439,420,0,438,429,501,519,5,518,509,521,539,3,538,529,481,499,4,498,489,695,687,699,686,626,633,625,627,264,646,653,265,645,647,606,613,266,605,607,546,553,267,545,547,566,573,268,565,567,586,593,269,585,587,456,457,440,270,441,473,466,271,465,467,433,426,272,425,427,506,513,273,505,507,526,533,274,525,527,486,493,275,485,487,702,685,690,689,623,630,622,624,118,643,650,119,642,644,603,610,117,602,604,543,550,114,542,544,563,570,115,562,564,583,590,116,582,584,454,455,444,109,445,470,463,110,462,464,430,423,108,422,424,503,510,112,502,504,523,530,113,522,524,483,490,111,482,484,694,696,693,692,30,298,80,56,142,31,299,143,78,54,32,297,141,79,55,33,294,138,83,59,34,295,139,81,57,35,296,140,82,58,75,289,28,133,51,290,29,134,76,52,288,27,132,77,53,24,292,136,74,50,25,293,137,72,48,26,291,135,73,49,678,684,663,683,91,304,406,42,215,92,305,213,407,43,90,303,214,405,44,94,300,211,402,45,95,301,212,403,46,93,302,210,404,47,397,310,89,206,40,311,87,204,398,41,309,88,205,396,39,85,306,209,400,36,86,307,207,401,37,84,308,208,399,38,676,670,662,681,12,358,382,128,239,13,359,237,383,126,14,357,238,381,127,15,354,235,378,131,16,355,236,379,129,17,356,234,380,130,373,349,18,230,123,350,19,228,374,124,348,20,229,372,125,21,352,233,376,122,22,353,231,377,120,23,351,232,375,121,671,675,668,673,203,144,187,157,177,201,145,178,188,158,202,146,179,186,156,199,147,176,190,160,200,148,174,191,161,198,149,175,189,159,185,150,194,168,163,151,192,169,183,164,152,193,170,184,162,197,153,171,181,166,195,154,172,182,167,196,155,173,180,165,679,667,680,666 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#5751a2f21b762bdcbb8d7ca8109ff664440cd913db63bda4230c3be52dd8f5e2, 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 17:26:28 · history