Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 172ce243844e…

magma 172ce243844e
Size
705
Isomorphism class hash
172ce243844eabcdd2047421439ba05cdf78ad246732b956928a3a456c8294e2
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 19:52:56
Display reorder
660,157,217,232,395,479,158,396,218,233,480,216,397,156,231,481,160,220,228,394,478,221,161,229,392,476,159,219,230,393,477,155,215,223,401,485,153,213,224,402,486,214,154,222,403,487,211,151,226,400,484,212,152,227,398,482,210,150,225,399,483,679,676,685,677,83,245,383,331,315,84,329,243,384,316,244,330,85,385,314,82,241,382,327,318,242,80,380,328,319,81,240,381,326,317,74,236,389,322,313,75,234,390,320,311,235,76,391,321,312,239,77,388,325,309,237,78,386,323,310,238,79,387,324,308,664,667,662,661,32,371,335,56,249,30,54,372,336,250,373,55,31,337,251,35,370,334,59,248,368,33,332,57,246,34,369,333,58,247,27,377,341,51,255,28,378,342,52,256,379,29,343,53,257,376,26,340,50,254,374,24,338,48,252,375,25,339,49,253,680,674,673,675,132,491,284,99,90,133,97,492,282,91,493,98,134,283,92,135,490,287,95,89,488,136,285,96,87,137,489,286,94,88,130,640,638,637,636,131,648,646,644,645,656,129,654,652,653,630,126,628,633,632,494,127,288,101,93,495,128,289,100,86,703,698,704,697,162,587,467,359,345,163,360,588,468,346,589,361,164,469,344,165,586,466,358,348,584,166,464,356,349,167,585,465,357,347,168,593,473,365,351,169,594,474,366,352,595,170,475,367,350,592,171,472,364,354,590,172,470,362,355,591,173,471,363,353,689,690,692,694,44,259,275,519,443,42,520,260,273,444,258,521,43,274,445,47,262,271,518,442,263,45,272,516,440,46,261,270,517,441,39,265,281,525,449,40,266,279,526,450,264,41,280,527,451,268,38,277,524,448,269,36,278,522,446,267,37,276,523,447,665,670,672,666,62,188,115,419,4,63,420,186,116,5,187,421,64,114,3,65,191,118,418,1,189,66,119,416,0,67,190,117,417,2,68,194,121,425,10,69,192,122,426,11,193,70,120,427,9,197,71,124,424,6,195,72,125,422,7,196,73,123,423,8,695,691,696,693,204,575,431,619,555,205,620,576,432,556,577,621,206,433,557,207,574,430,618,554,572,208,428,616,552,209,573,429,617,553,202,581,437,625,561,203,582,438,626,562,583,201,439,627,563,580,198,436,624,560,578,199,434,622,558,579,200,435,623,559,682,688,678,684,299,500,611,567,292,300,568,501,612,290,502,569,301,613,291,298,499,610,566,295,497,296,608,564,293,297,498,609,565,294,305,641,643,642,639,306,649,651,650,647,657,307,659,658,655,634,304,635,631,629,503,302,614,570,60,496,303,615,571,61,701,700,702,699,13,531,455,507,407,14,508,532,456,408,533,509,12,457,409,16,530,454,506,406,528,17,452,504,404,15,529,453,505,405,19,537,461,513,413,20,538,462,514,414,539,18,463,515,415,536,22,460,512,412,534,23,458,510,410,535,21,459,511,411,663,669,668,671,113,543,141,185,599,111,183,544,142,600,545,184,112,143,601,109,542,140,181,598,540,110,138,182,596,108,541,139,180,597,104,549,147,176,605,102,550,148,174,606,551,103,149,175,607,548,107,146,179,604,546,105,144,177,602,547,106,145,178,603,686,687,683,681 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#b2f3cd20f8767e98b3e6e1e1383f90e37f2ce11df778eec5ffdbe92cabb78104, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 19:52:57 · history