Equation 677 Database

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Magma cfefddae5b4b…

magma cfefddae5b4b
Size
381
Isomorphism class hash
cfefddae5b4b78332a64a401cb79e6fe05b2296d00bf6d9cb699cbb88dcad9e7
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 23:33:12
Display reorder
380,85,84,86,87,88,83,196,201,206,180,185,190,283,293,80,81,82,273,225,230,236,210,215,220,245,251,256,261,266,240,106,101,102,103,104,105,90,91,92,93,94,89,95,96,97,98,99,100,155,160,166,171,176,150,275,285,295,140,145,135,304,303,302,305,301,300,346,369,333,343,330,378,354,363,373,355,17,22,18,19,20,21,199,204,209,184,189,194,281,291,44,45,46,270,229,234,239,214,219,224,249,254,259,264,269,244,2,3,4,5,6,0,15,16,13,14,1,134,11,12,7,8,9,10,159,164,169,174,179,154,279,289,299,144,149,139,318,323,322,319,320,321,349,367,336,331,335,376,350,361,370,359,64,63,65,66,67,62,198,203,208,183,188,193,282,292,59,60,61,272,228,233,238,213,218,223,248,253,258,263,268,243,58,53,54,55,56,57,69,70,71,72,73,68,74,75,76,77,78,79,158,163,168,173,178,153,278,288,298,143,148,138,325,324,329,326,327,328,347,368,334,341,337,377,353,362,372,358,125,124,126,127,122,123,197,202,207,182,187,192,284,294,120,121,119,274,227,232,237,212,217,222,247,252,257,262,267,242,114,115,116,117,118,113,131,132,133,128,129,130,109,110,111,112,107,108,157,162,167,172,177,152,277,287,297,142,147,137,307,306,311,308,309,310,348,366,332,342,344,379,352,364,374,357,52,51,47,48,49,50,195,200,205,181,186,191,280,290,42,43,23,271,226,231,235,211,216,221,246,250,255,260,265,241,36,37,38,39,40,41,29,24,25,26,27,28,31,32,33,34,35,30,156,161,165,170,175,151,276,286,296,141,146,136,314,313,312,315,316,317,345,365,339,338,340,375,351,360,371,356 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 = {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 23:33:13 · history