Equation 677 Database

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Magma c5982ecc6d29…

magma c5982ecc6d29
Size
381
Isomorphism class hash
c5982ecc6d29fda0bf08727cd433ea95d77dfde1d549f1f143360151e9c6cf6d
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 23:51:05
Display reorder
380,308,307,306,310,311,309,96,230,91,80,85,75,5,6,7,8,9,235,215,205,210,201,191,195,248,251,243,261,267,256,186,176,181,170,160,165,220,31,26,41,45,36,135,140,130,151,156,146,272,278,281,286,290,295,101,107,113,115,120,126,51,61,56,71,65,226,341,361,350,335,356,345,376,370,330,365,312,314,313,317,315,316,98,233,93,83,88,78,20,21,22,23,24,239,219,209,214,204,194,199,249,254,244,264,269,259,189,179,184,174,164,169,223,34,28,43,48,38,139,144,134,154,159,149,274,279,284,289,294,299,104,109,112,119,124,129,53,63,58,73,68,228,343,364,354,338,359,348,379,374,334,369,303,305,304,302,301,300,99,234,94,84,89,79,3,4,2,1,0,236,218,208,213,203,193,198,246,250,240,263,265,255,188,178,183,173,163,168,224,33,29,44,49,39,138,143,133,153,158,148,270,276,280,288,293,298,103,105,111,118,123,128,54,64,59,74,69,229,344,363,351,339,358,349,378,373,333,368,323,322,321,319,320,318,97,232,92,82,87,77,15,16,17,18,19,238,217,207,212,202,192,197,245,253,241,262,268,258,187,177,182,172,162,167,222,32,27,42,47,37,137,142,132,152,157,147,271,275,283,287,292,297,102,108,110,117,122,127,52,62,57,72,67,227,342,362,353,337,357,347,377,372,332,367,329,328,327,325,326,324,95,231,90,81,86,76,10,11,12,13,14,237,216,206,211,200,190,196,247,252,242,260,266,257,185,175,180,171,161,166,221,30,25,40,46,35,136,141,131,150,155,145,273,277,282,285,291,296,100,106,114,116,121,125,50,60,55,70,66,225,340,360,352,336,355,346,375,371,331,366 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#fac090d670a9c14492c148fae382a21bad3e48687c67df8555101af0e65e1711, M = {72} 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 23:51:06 · history