Equation 677 Database

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Magma ff78ce4b780f…

magma ff78ce4b780f
Size
381
Isomorphism class hash
ff78ce4b780fd640928630c9085c6e57509c5480614e22ca7004cc8fbdaeb91b
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 23:32:56
Display reorder
380,321,320,322,323,318,319,240,245,250,255,231,235,284,294,126,127,264,274,136,141,145,150,155,131,107,108,103,104,105,106,176,181,186,160,165,170,297,197,192,267,277,287,111,112,109,129,113,110,121,122,123,124,125,120,215,220,225,201,206,211,117,116,115,118,119,114,350,342,332,334,364,374,355,365,349,376,326,325,327,328,329,324,243,248,253,258,233,238,281,291,45,46,260,270,139,144,148,153,158,133,10,11,12,7,8,9,178,183,188,163,169,174,299,199,194,269,279,289,13,14,15,16,17,18,0,2,3,4,5,6,218,223,228,203,208,213,19,24,23,20,21,22,339,353,331,351,362,372,359,368,338,378,301,305,300,302,303,304,242,247,252,257,232,237,282,292,69,70,262,272,137,142,147,152,157,132,73,74,75,76,71,72,177,182,187,162,167,172,296,196,190,265,275,286,56,57,58,53,54,55,68,65,1,128,66,67,217,222,227,202,207,212,60,59,64,61,62,63,333,344,337,343,363,373,357,367,345,377,308,307,309,310,311,306,244,249,254,259,234,239,280,290,43,44,261,271,138,143,149,154,159,134,49,50,51,52,47,48,179,184,189,164,168,173,298,198,193,268,278,288,26,27,28,29,30,25,38,39,40,41,42,37,219,224,229,204,209,214,34,33,32,35,36,31,341,354,335,352,360,371,358,369,340,379,312,317,313,314,315,316,241,246,251,256,230,236,283,293,84,83,263,273,135,140,146,151,156,130,82,77,78,79,80,81,175,180,185,161,166,171,295,195,191,266,276,285,86,87,88,89,90,85,98,99,100,101,102,97,216,221,226,200,205,210,94,93,92,95,96,91,348,336,347,330,361,370,356,366,346,375 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 = {68} 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 23:32:57 · history