Equation 677 Database

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Magma 83aca495dfe5…

magma 83aca495dfe5
Size
381
Isomorphism class hash
83aca495dfe5b61b75c99f9545601da937a062a91217d0e31758f9ca5092cc3b
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:36:42
Display reorder
380,274,269,264,254,249,239,244,234,224,229,219,259,303,304,305,301,300,302,289,214,209,199,204,194,119,109,114,134,124,129,144,284,139,159,149,154,164,169,174,179,184,189,294,24,18,9,14,4,49,54,44,34,39,29,74,79,279,59,64,69,104,299,99,89,94,84,349,344,354,359,334,339,378,364,369,374,271,266,260,251,246,235,240,230,221,226,215,256,316,317,315,313,314,312,286,210,205,197,201,190,117,105,112,130,120,125,141,280,136,155,146,150,160,165,170,176,181,186,290,21,15,5,10,0,45,50,40,31,36,26,70,75,276,56,61,66,102,297,97,85,92,80,347,340,351,356,331,337,375,360,365,370,273,268,263,253,248,238,243,233,223,228,218,258,321,322,323,318,319,320,287,212,207,196,202,192,115,107,110,132,121,127,142,282,137,157,147,152,162,167,172,177,182,187,293,23,17,8,13,3,48,53,43,33,38,28,73,78,278,58,63,68,101,295,96,86,90,81,345,343,353,358,332,336,376,362,368,373,270,265,261,250,245,236,241,231,220,225,216,255,324,325,326,327,328,329,285,211,206,195,200,191,116,106,111,131,122,126,140,281,135,156,145,151,161,166,171,175,180,185,291,20,16,6,11,1,46,51,41,30,35,25,71,76,275,55,60,65,100,296,95,87,91,82,346,341,350,355,330,335,379,361,366,371,272,267,262,252,247,237,242,232,222,227,217,257,306,307,308,309,310,311,288,213,208,198,203,193,118,108,113,133,123,128,143,283,138,158,148,153,163,168,173,178,183,188,292,22,19,7,12,2,47,52,42,32,37,27,72,77,277,57,62,67,103,298,98,88,93,83,348,342,352,357,333,338,377,363,367,372 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#9acf37934a26f07a9500b1ccb24642817fa617552582595ca38f94c8a1f3c019, M = {76} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:36:42 · history