Equation 677 Database

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Magma bdc4b874902a…

magma bdc4b874902a
Size
381
Isomorphism class hash
bdc4b874902a647b483625d36f8cf8b7203c6b77c7f2f45d27c1eef5a942a943
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 23:49:59
Display reorder
380,154,164,159,179,169,174,194,184,189,209,199,204,11,277,10,52,57,47,268,258,263,253,240,246,119,294,124,104,105,110,214,219,224,227,232,237,149,299,144,134,139,129,324,325,326,327,328,329,70,61,67,82,77,282,23,32,27,42,37,272,0,7,286,87,90,95,358,337,342,350,332,364,367,347,374,377,151,160,155,177,166,171,191,180,185,206,197,202,3,275,2,51,56,46,267,256,261,251,243,248,118,293,123,103,109,114,212,217,222,226,231,236,148,298,143,133,138,128,318,319,320,321,322,323,71,60,65,81,76,280,22,34,26,40,36,270,9,8,287,85,92,97,357,335,340,352,330,363,366,345,372,375,153,163,158,178,168,173,193,183,188,208,198,203,15,278,14,53,58,48,265,255,260,250,241,245,115,291,122,100,108,112,213,218,223,228,233,238,147,297,142,132,137,127,310,311,309,307,308,306,73,63,68,83,78,283,21,31,28,43,38,273,13,12,288,88,93,98,356,338,343,353,333,362,368,348,373,378,152,162,157,176,167,172,192,182,187,205,195,200,19,279,18,54,59,49,269,259,264,254,244,249,117,292,120,101,106,111,211,216,221,229,234,239,145,295,140,131,136,126,312,313,314,315,316,317,74,64,69,84,79,284,24,33,29,44,39,274,17,16,289,89,94,99,355,339,344,354,334,360,369,349,371,379,150,161,156,175,165,170,190,181,186,207,196,201,1,276,4,50,55,45,266,257,262,252,242,247,116,290,121,102,107,113,210,215,220,225,230,235,146,296,141,130,135,125,303,304,305,301,300,302,72,62,66,80,75,281,20,30,25,41,35,271,6,5,285,86,91,96,359,336,341,351,331,361,365,346,370,376 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#edf00a573dad398077d9e9a7f74ac5f2ae5601c41b127cdfd29539dca9f6b98a, M = {74} 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 23:50:00 · history