Equation 677 Database

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Magma dce9574d65d7…

magma dce9574d65d7
Size
381
Isomorphism class hash
dce9574d65d7b76591602f988e5c3b97e12c4378558d924865912ea25600d7a7
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 23:50:53
Display reorder
380,50,298,51,49,48,52,163,153,158,178,168,173,85,90,82,73,78,283,213,46,273,8,9,47,53,54,55,56,243,57,288,233,238,228,218,223,323,321,322,320,318,319,148,138,143,133,123,128,193,183,188,208,198,203,263,268,278,248,253,258,103,98,293,113,118,108,353,348,343,333,364,358,373,368,338,378,62,299,63,61,60,64,164,154,159,179,169,174,86,91,83,74,79,284,214,58,274,3,2,59,65,66,67,68,244,69,289,234,239,229,219,224,316,317,315,313,314,312,149,139,144,134,124,129,194,184,189,209,199,204,264,269,279,249,254,259,104,99,294,114,119,109,354,349,344,334,363,359,374,369,339,379,38,297,39,37,36,40,162,152,157,177,167,172,87,92,80,72,77,282,211,33,270,32,30,31,41,42,43,44,242,45,286,231,236,225,217,220,324,325,326,327,328,329,147,137,142,132,122,127,192,182,187,207,197,202,262,267,277,247,252,257,102,97,292,112,117,107,352,347,342,332,362,357,372,367,336,377,4,296,23,7,5,6,161,151,156,175,165,170,89,93,81,71,76,280,212,34,272,0,35,1,25,26,24,28,240,27,285,230,235,226,216,221,308,306,307,311,309,310,145,136,141,130,120,125,190,180,185,206,196,201,261,266,275,245,250,255,101,96,290,110,116,105,350,345,340,331,360,356,371,366,337,375,21,295,22,20,18,19,160,150,155,176,166,171,88,94,84,70,75,281,210,10,271,13,11,12,15,29,14,17,241,16,287,232,237,227,215,222,303,304,305,301,300,302,146,135,140,131,121,126,191,181,186,205,195,200,260,265,276,246,251,256,100,95,291,111,115,106,351,346,341,330,361,355,370,365,335,376 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 = {69} 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 23:50:54 · history