Equation 677 Database

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Magma 6f39f9012e5d…

magma 6f39f9012e5d
Size
399
Isomorphism class hash
6f39f9012e5d125d623fe73168bae8154cf08b0512fe9abe9fd062676014f8d0
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
2026-10-08 14:02:57
Display reorder
50,51,52,53,45,46,47,48,49,43,44,36,37,38,39,40,41,42,381,327,82,316,298,328,83,299,317,329,84,300,318,330,85,301,319,331,86,302,320,332,87,303,321,324,88,304,322,325,89,305,323,326,81,297,315,75,336,291,309,76,337,292,310,77,338,293,311,78,339,294,312,79,340,295,313,80,341,296,314,72,333,288,306,73,334,289,307,74,335,290,308,391,385,386,392,287,114,200,263,279,115,264,201,280,116,265,202,281,108,266,203,282,109,267,204,283,110,268,205,284,111,269,206,285,112,261,198,286,113,262,199,123,271,256,209,124,272,257,210,125,273,258,211,117,274,259,212,118,275,260,213,119,276,252,214,120,277,253,215,121,278,254,207,122,270,255,208,383,389,390,384,190,56,226,127,191,57,128,227,192,58,129,228,193,59,130,229,194,60,131,230,195,61,132,231,196,62,133,232,197,54,134,233,189,55,126,225,65,183,136,219,66,184,137,220,67,185,138,221,68,186,139,222,69,187,140,223,70,188,141,224,71,180,142,216,63,181,143,217,64,182,135,218,388,398,397,387,348,178,342,101,350,179,102,344,352,171,103,346,354,172,104,349,356,173,105,351,358,174,106,353,343,175,107,355,345,176,99,357,347,177,100,359,162,366,94,361,163,368,95,363,164,370,96,365,165,373,97,367,166,375,98,369,167,377,90,371,168,360,91,372,169,362,92,374,170,364,93,376,394,395,396,393,4,144,237,25,5,145,26,238,6,146,18,239,7,147,19,240,8,148,20,241,1,149,21,242,0,150,22,234,2,151,23,235,3,152,24,236,153,13,34,246,154,14,35,247,155,15,27,248,156,16,28,249,157,17,29,250,158,9,30,251,159,10,31,243,160,11,32,244,161,12,33,245,380,379,378,382 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#42868235e501604e29e4278fa2f6eb80ea45b953482e06247fa1c96182459712, 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 2026-10-08 14:02:58 · history