Equation 677 Database

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Magma 553c9da5af91…

magma 553c9da5af91
Size
381
Isomorphism class hash
553c9da5af91650ee5671cd2210f561f61e41e6598ff5556a37d403f8420772b
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 23:25:19
Display reorder
380,2,0,3,4,5,1,146,120,125,130,135,141,190,195,201,206,180,185,106,111,116,90,95,101,286,291,296,270,276,281,323,318,319,320,321,322,256,261,266,240,245,250,86,60,65,70,75,81,51,56,30,35,41,46,151,161,175,166,170,156,210,220,236,226,231,215,342,357,340,374,338,339,379,364,332,368,13,12,14,15,16,17,147,122,127,132,137,142,192,197,202,207,182,187,107,112,117,92,97,102,287,292,297,272,277,282,327,328,329,324,325,326,257,262,267,242,247,252,87,62,67,72,77,82,52,57,32,37,42,47,152,162,177,167,172,157,212,222,237,227,232,217,349,358,333,370,350,336,376,361,341,367,25,24,26,27,28,29,149,124,129,134,139,144,194,199,204,209,184,189,109,114,119,94,99,104,289,294,299,274,279,284,312,313,314,315,316,317,259,264,269,244,249,254,89,64,69,74,79,84,54,59,34,39,44,49,150,160,176,165,171,155,214,224,239,229,234,219,353,356,331,371,354,348,375,360,330,366,7,6,8,9,10,11,145,121,126,131,136,140,191,196,200,205,181,186,105,110,115,91,96,100,285,290,295,271,275,280,309,310,311,306,307,308,255,260,265,241,246,251,85,61,66,71,76,80,50,55,31,36,40,45,154,164,179,169,174,159,211,221,235,225,230,216,346,355,345,373,347,344,378,363,337,365,19,18,20,21,22,23,148,123,128,133,138,143,193,198,203,208,183,188,108,113,118,93,98,103,288,293,298,273,278,283,302,303,304,305,301,300,258,263,268,243,248,253,88,63,68,73,78,83,53,58,33,38,43,48,153,163,178,168,173,158,213,223,238,228,233,218,351,359,334,372,352,343,377,362,335,369 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#4ff69c35f55aa106c20b4528e074e3f72eddedd150e00069ea529e91bc9e2010, M = {73} 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 23:25:20 · history