Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma e3b6fbc2a392…

magma e3b6fbc2a392
Size
705
Isomorphism class hash
e3b6fbc2a392241a0b021e2ad11a5786e43d93cb88e5e33ce06400fe260ebfe3
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 17:18:48
Display reorder
660,615,48,608,618,601,635,49,628,638,621,655,50,648,658,640,51,595,588,598,580,52,555,548,558,541,53,575,568,578,560,428,435,54,438,420,448,454,55,456,442,468,475,56,478,461,495,488,57,498,481,515,508,58,518,501,535,528,59,538,520,686,694,698,688,606,107,600,614,605,626,105,620,634,625,646,106,641,654,645,103,586,581,594,585,104,546,540,554,545,102,566,561,574,565,421,426,98,434,425,441,446,96,453,445,460,466,97,474,465,486,480,101,494,485,506,500,99,514,505,526,521,100,534,525,695,692,699,687,108,91,174,20,405,109,92,175,18,406,110,90,176,19,407,94,111,177,23,404,95,112,178,21,402,93,113,179,22,403,172,114,89,15,396,173,115,87,16,397,171,116,88,17,398,117,168,85,14,399,118,169,86,12,400,119,170,84,13,401,665,680,678,663,345,194,228,218,206,346,192,229,216,204,347,193,230,217,205,197,344,231,221,209,195,342,232,219,207,196,343,233,220,208,234,336,200,224,212,235,337,198,222,210,236,338,199,223,211,339,237,203,227,215,340,238,201,225,213,341,239,202,226,214,668,675,673,671,613,25,610,604,617,633,26,630,624,637,653,24,650,644,657,28,593,590,584,597,29,553,550,544,557,27,573,570,564,577,430,433,31,424,437,450,458,32,457,459,470,473,30,464,477,493,490,34,484,497,513,510,35,504,517,533,530,33,524,537,700,685,703,702,603,76,619,607,609,623,77,639,627,629,643,75,659,647,649,72,583,599,587,589,73,543,559,547,549,74,563,579,567,569,439,423,82,427,429,440,444,83,447,449,479,463,81,467,469,483,499,78,487,489,503,519,79,507,509,523,539,80,527,529,704,689,696,701,611,43,616,602,612,631,44,636,622,632,651,42,656,642,652,46,591,596,582,592,47,551,556,542,552,45,571,576,562,572,436,431,41,422,432,455,451,39,443,452,476,471,40,462,472,491,496,37,482,492,511,516,38,502,512,531,536,36,522,532,690,693,691,697,321,269,261,251,417,322,267,262,249,418,323,268,263,250,419,265,320,260,247,416,266,318,258,248,414,264,319,259,246,415,252,312,275,242,408,253,313,273,240,409,254,314,274,241,410,315,255,271,245,411,316,256,272,243,412,317,257,270,244,413,681,684,670,661,124,65,333,297,357,125,63,334,298,358,123,64,335,299,359,61,120,332,296,356,62,121,330,294,354,60,122,331,295,355,324,130,71,288,348,325,131,69,289,349,326,129,70,290,350,126,327,67,291,351,127,328,68,292,352,128,329,66,293,353,666,674,683,672,145,165,191,369,393,146,166,189,370,394,144,167,190,371,395,164,148,187,368,392,162,149,188,366,390,163,147,186,367,391,182,151,156,360,384,180,152,157,361,385,181,150,158,362,386,154,185,159,363,387,155,183,160,364,388,153,184,161,365,389,676,679,662,669,309,141,7,282,381,310,142,8,283,382,311,143,6,284,383,140,308,10,285,380,138,306,11,286,378,139,307,9,287,379,5,300,132,280,372,3,301,133,281,373,4,302,134,279,374,303,0,135,276,375,304,2,136,277,376,305,1,137,278,377,664,677,667,682 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#4dbd6b0006d3996c22611f6a9a74b6d8666415e8467cb95ff3380ed5b17e9234, 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 17:18:49 · history