Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma bec633053a3c…

magma bec633053a3c
Size
705
Isomorphism class hash
bec633053a3cd7fdf04acd71b035ecb55d1d7a5808cedf3e97b9e36cbe2ec1c3
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 18:09:50
Display reorder
660,592,145,582,593,580,552,146,542,553,541,572,144,562,573,560,652,148,653,640,642,612,149,602,613,601,632,147,622,633,621,482,492,493,151,481,502,512,513,152,501,522,532,533,150,520,472,464,473,154,460,429,423,437,155,436,153,452,444,453,441,693,685,691,696,596,23,588,598,599,556,21,548,558,559,576,22,568,579,578,656,19,659,658,648,616,20,608,618,619,636,18,628,639,638,488,496,498,14,499,508,516,518,12,519,528,536,539,13,538,476,468,478,17,479,431,425,438,15,439,16,456,448,459,458,689,700,697,688,412,68,110,98,413,409,66,108,96,408,410,67,109,97,411,418,71,101,419,113,415,69,111,99,414,416,70,112,100,417,116,403,104,63,402,114,405,102,64,404,115,406,103,65,407,400,119,107,62,401,396,117,105,60,397,61,398,118,106,399,677,683,684,681,356,173,164,143,392,354,171,162,141,390,355,172,163,142,391,359,169,139,395,167,357,170,165,140,393,358,168,166,138,394,159,351,134,179,387,160,352,132,177,388,161,353,133,178,389,350,158,137,175,386,348,156,135,176,384,174,349,157,136,385,682,680,672,676,597,73,583,589,595,557,74,543,549,555,577,72,563,569,575,657,76,649,655,643,617,77,603,609,615,637,75,623,629,635,483,497,489,79,495,503,517,509,80,515,523,537,529,78,535,477,462,469,82,475,435,433,426,83,430,81,457,442,449,455,687,694,698,702,581,42,594,585,591,540,43,554,545,551,561,44,574,565,571,641,45,645,651,654,600,46,614,605,611,620,47,634,625,631,494,480,485,40,491,514,500,505,41,511,534,521,525,39,531,461,474,465,36,471,432,434,424,37,428,38,440,454,445,451,699,690,695,686,584,180,590,587,586,544,181,550,547,546,564,182,570,567,566,644,183,647,646,650,604,184,610,607,606,624,185,630,627,626,490,484,487,186,486,510,504,507,187,506,530,524,527,188,526,463,470,467,189,466,422,427,421,190,420,191,443,450,447,446,701,704,703,692,27,271,86,320,284,28,272,84,318,282,29,270,85,319,283,26,274,323,287,89,24,275,87,321,285,25,273,88,322,286,92,33,315,269,279,90,34,316,267,280,91,35,317,268,281,32,95,314,265,278,30,93,312,266,276,264,31,94,313,277,667,664,679,662,213,127,332,237,225,214,128,330,238,226,215,126,331,239,227,212,130,236,224,335,210,131,333,234,222,211,129,334,235,223,327,204,228,125,216,328,205,229,123,217,329,206,230,124,218,207,326,231,121,219,208,324,232,122,220,120,209,325,233,221,673,668,669,670,260,7,296,51,380,258,8,294,52,378,259,6,295,53,379,263,10,50,383,299,261,11,297,48,381,262,9,298,49,382,291,255,57,5,375,292,256,58,3,376,293,257,59,4,377,254,290,56,0,374,252,288,54,2,372,1,253,289,55,373,675,678,663,665,308,203,368,344,248,306,201,366,342,246,307,202,367,343,247,311,199,347,251,371,309,200,369,345,249,310,198,370,346,250,363,303,339,194,243,364,304,340,192,244,365,305,341,193,245,302,362,338,197,242,300,360,336,195,240,196,301,361,337,241,671,661,666,674 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#676093fc8b0a9c703c9b4a913f63a03a075a7ec27635c2c42c5b015ba025ae64, 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 18:09:51 · history