Equation 677 Database

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Magma 63b0ba910fee…

magma 63b0ba910fee
Size
361
Isomorphism class hash
63b0ba910fee7c474d71fb4a49b069de82b739c78db3914dc0fa67b176e965df
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Fiber matrix
symmetric: yes · normal: yes · rank: 361 (nullity 0) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:10:35
Display reorder
291,301,322,349,308,314,306,340,310,359,295,300,307,342,321,351,325,348,296,316,344,354,336,357,360,304,332,303,328,312,320,339,353,341,293,302,313,299,356,289,324,350,330,355,319,305,345,317,333,298,323,347,358,343,311,318,331,329,294,327,346,326,292,352,337,338,288,334,335,297,315,309,290,250,76,80,252,217,187,34,30,68,83,61,144,47,238,195,248,56,107,26,55,169,132,240,222,103,266,148,245,59,15,216,139,93,43,198,234,41,141,143,109,82,221,179,39,277,71,192,131,145,6,160,272,280,209,91,36,243,202,2,171,231,108,156,128,11,176,88,208,229,259,184,21,197,72,96,281,215,155,81,112,14,49,92,233,1,201,170,158,27,110,105,44,151,104,276,225,77,152,244,183,87,20,251,24,86,10,218,175,78,121,48,100,74,194,200,0,228,38,178,133,275,50,220,283,161,285,29,70,261,254,125,186,269,123,273,137,117,212,5,227,236,191,264,64,189,136,7,257,210,159,42,79,18,119,120,282,16,157,232,182,102,126,115,73,165,52,149,223,90,239,287,284,40,63,286,135,130,99,180,242,54,31,62,58,25,188,206,95,213,97,268,3,168,33,172,262,153,203,12,113,207,177,22,147,255,66,260,122,116,162,17,241,196,258,199,106,174,124,23,246,219,146,67,19,9,118,127,263,32,205,185,214,89,114,111,45,164,46,230,224,134,150,270,226,8,57,279,101,98,85,211,190,51,4,28,75,69,173,204,94,235,84,163,60,271,65,193,267,166,249,13,138,265,247,53,154,253,35,274,142,129,181,37,237,256,167,278,140 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 361 = 1 + 5*72, 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#882574997286180eb67ca1c7e27992d77d3597f78b7f59bc1c9a77bfc81a519f, M = {0} 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, 72): MacNeish's product over GF(8) x GF(9); GF(8) = F_2[x]/(x^3 + x + 1), GF(9) = F_3[x]/(x^2 + 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: 361.

last edited by qawbecrdtey at 2026-10-01 23:10:36 · history