Equation 677 Database

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Magma 7515b71f89a6…

magma 7515b71f89a6
Size
399
Isomorphism class hash
7515b71f89a67636227c078e83191c9dc47ca035e8fc4ae6435a28a68e7b98ff
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 21:15:01
Display reorder
306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,379,327,60,294,74,328,75,61,295,329,76,62,296,330,77,54,288,331,78,55,289,332,79,56,290,324,80,57,291,325,72,58,292,326,73,59,293,336,83,69,303,84,337,70,304,85,338,71,305,86,339,63,297,87,340,64,298,88,341,65,299,333,89,66,300,334,81,67,301,335,82,68,302,391,385,386,392,259,222,274,119,260,120,223,275,252,121,224,276,253,122,216,277,254,123,217,278,255,124,218,270,256,125,219,271,257,117,220,272,258,118,221,273,268,112,231,283,113,269,232,284,114,261,233,285,115,262,225,286,116,263,226,287,108,264,227,279,265,109,228,280,266,110,229,281,267,111,230,282,383,389,390,384,0,99,133,176,2,177,100,134,3,178,101,126,4,179,102,127,5,171,103,128,6,172,104,129,7,173,105,130,8,174,106,131,1,175,107,132,10,169,92,142,170,11,93,143,162,12,94,135,163,13,95,136,164,14,96,137,165,15,97,138,16,166,98,139,17,167,90,140,9,168,91,141,388,398,397,387,348,244,342,208,350,209,245,344,352,210,246,346,354,211,247,349,356,212,248,351,358,213,249,353,343,214,250,355,345,215,251,357,347,207,243,359,367,201,237,360,202,369,238,362,203,371,239,364,204,372,240,366,205,374,241,368,206,376,242,370,361,198,234,373,363,199,235,375,365,200,236,377,394,395,396,393,36,161,24,193,37,194,153,25,38,195,154,26,39,196,155,18,40,197,156,19,41,189,157,20,42,190,158,21,43,191,159,22,44,192,160,23,45,186,145,33,187,46,146,34,188,47,147,35,180,48,148,27,181,49,149,28,182,50,150,29,51,183,151,30,52,184,152,31,53,185,144,32,381,380,378,382 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#47a7004ec900b2701b5e0d8d5f3b4294b663f23eefba7ecd1a93ec284618a003, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 21.

last edited by qawbecrdtey at 2026-10-07 21:15:02 · history