Equation 677 Database

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Magma c12fb1b6c01e…

magma c12fb1b6c01e
Size
381
Isomorphism class hash
c12fb1b6c01e52c065b5b9174ecffc20059844cc4ee66169d89cad9a0181f121
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 23:32:44
Display reorder
380,74,73,75,76,77,72,63,64,65,60,61,62,85,86,87,88,89,84,81,82,83,78,79,80,305,301,300,302,303,304,267,242,247,252,257,262,217,222,227,232,237,212,207,182,187,192,197,202,271,276,281,286,291,296,150,155,160,165,170,175,69,68,67,70,71,66,330,336,358,377,347,333,352,364,372,368,39,38,40,41,36,37,55,56,57,58,59,54,51,52,53,48,49,50,47,42,43,44,45,46,307,308,309,310,311,306,268,243,248,254,259,264,218,224,229,234,238,213,208,183,188,194,199,204,274,278,284,289,294,299,154,159,164,169,174,178,32,31,30,33,34,35,340,341,356,376,348,342,354,361,371,365,118,117,119,114,115,116,104,105,106,107,102,103,96,97,98,99,100,101,92,93,94,95,90,91,314,315,316,317,312,313,265,241,246,251,256,261,216,221,225,230,235,211,205,181,185,190,195,200,270,275,280,285,290,295,151,156,161,166,171,176,109,108,113,110,111,112,332,337,359,378,346,331,350,360,373,369,127,126,128,129,130,131,149,144,145,146,147,148,140,141,142,143,138,139,136,137,132,133,134,135,327,328,329,324,325,326,269,244,249,253,258,263,219,223,228,233,239,214,209,184,189,193,198,203,273,279,283,288,293,298,153,158,163,168,173,179,120,125,124,121,122,123,343,335,355,375,349,344,353,362,370,366,8,7,9,10,11,6,24,25,26,27,28,29,19,20,21,22,23,18,15,16,17,12,13,14,321,322,323,318,319,320,266,240,245,250,255,260,215,220,226,231,236,210,206,180,186,191,196,201,272,277,282,287,292,297,152,157,162,167,172,177,3,2,0,4,5,1,338,334,357,379,345,339,351,363,374,367 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#81fb02f374018e52eb43ccfa7482c1ceb3842f71095f08d9a76873470f8f397e, M = {66} 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 23:32:45 · history