Equation 677 Database

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Magma 10a09232685b…

magma 10a09232685b
Size
595
Isomorphism class hash
10a09232685b65687f85fb56945bf430cb2a9a93a76fec71fcd71dc4aeab07c3
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-09 01:59:52
Display reorder
41,43,42,46,44,45,60,59,61,64,62,63,151,150,152,153,154,155,394,393,395,390,391,392,480,485,481,482,483,484,515,535,518,573,586,164,163,162,165,166,167,78,77,79,149,80,81,175,174,176,177,178,179,161,160,159,156,157,158,187,195,191,183,256,253,230,232,231,234,235,233,227,249,226,236,229,228,26,28,27,24,25,23,357,356,358,359,354,355,312,317,313,314,315,316,269,268,264,265,266,267,444,449,445,446,447,448,335,334,330,331,332,333,376,375,377,372,373,374,477,476,478,479,474,475,471,470,472,473,468,469,534,550,511,539,537,536,543,549,578,590,593,558,570,557,585,556,215,214,216,219,217,218,244,243,245,248,246,247,250,254,180,185,189,193,55,54,53,56,57,58,85,87,86,84,82,83,33,32,34,31,29,30,91,90,89,93,94,92,208,210,209,212,213,211,487,486,488,489,490,491,443,442,438,439,440,441,417,416,418,419,414,415,504,509,505,506,507,508,371,370,366,367,368,369,420,425,421,422,423,424,337,336,338,339,340,341,275,274,270,271,272,273,552,523,546,540,547,517,520,512,580,587,591,575,583,566,559,571,125,127,126,123,124,122,171,170,172,169,168,173,145,144,143,141,142,140,103,102,101,104,105,106,8,7,6,10,11,9,72,71,73,76,74,75,15,88,16,14,12,13,111,110,112,115,113,114,311,310,306,307,308,309,463,462,464,465,466,467,502,501,503,498,499,500,361,360,362,363,364,365,455,454,450,451,452,453,302,301,303,304,305,300,283,282,284,285,286,287,296,295,297,298,299,294,538,522,525,531,527,532,513,521,594,563,574,562,582,572,560,564,223,225,224,221,222,220,202,204,203,206,207,205,252,257,181,186,190,194,97,96,95,98,99,100,131,133,132,130,128,129,20,22,21,18,19,17,37,36,35,39,40,38,107,109,108,146,147,148,288,293,289,290,291,292,385,384,386,387,388,389,434,433,435,436,437,432,397,396,398,399,400,401,496,495,497,492,493,494,261,260,262,263,259,258,346,345,347,342,343,344,404,403,405,406,407,402,545,514,533,541,548,524,529,510,592,554,584,576,579,569,565,589,0,1,2,5,3,4,66,65,67,70,68,69,49,48,47,51,52,50,119,121,120,117,118,116,184,192,188,182,255,251,199,201,200,197,198,196,240,242,241,239,237,238,137,139,138,135,136,134,321,320,322,323,318,319,457,456,458,459,460,461,430,429,431,426,427,428,281,280,276,277,278,279,351,350,352,353,348,349,383,382,378,379,380,381,412,411,413,408,409,410,326,325,327,328,329,324,519,551,530,516,528,526,542,544,553,555,567,568,581,561,577,588 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#f04ca8125d7ce546c7552606527b36663a07f654279810fba8dfdb3271b338ee, M = the submagma generated by {0, 12} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-09 01:59:53 · history