Equation 677 Database

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Magma f7fdbe45701f…

magma f7fdbe45701f
Size
321
Isomorphism class hash
f7fdbe45701f69372d20b70c1c17a2c83f33a5ac5271c8ba2f60e1dcc53dc072
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:26:57
Display reorder
300,90,51,217,143,29,88,52,215,144,27,89,50,216,142,28,54,86,213,139,25,55,87,214,140,26,85,53,212,141,24,96,134,57,223,35,94,135,58,221,33,95,133,56,222,34,137,92,60,219,31,138,93,61,220,32,136,91,59,218,30,304,311,301,305,273,272,274,251,275,265,264,266,249,267,269,268,270,250,271,257,256,258,247,259,261,260,262,248,263,252,253,254,246,255,296,242,297,298,299,288,240,289,290,291,292,241,293,294,295,245,280,281,282,283,243,285,284,286,287,244,276,277,278,279,318,320,319,317,200,206,148,18,2,198,204,149,19,1,199,205,150,20,0,202,196,147,21,5,203,197,145,22,3,195,201,146,23,4,237,16,238,154,8,37,17,210,155,6,36,15,211,156,7,12,194,208,153,11,13,192,209,151,9,14,193,207,152,10,303,307,313,314,174,102,168,115,229,172,100,166,116,227,173,101,167,117,228,98,170,164,118,225,99,171,165,119,226,169,97,163,120,224,180,113,108,159,235,178,114,106,157,233,179,112,107,158,234,109,176,104,162,231,110,177,105,160,232,111,175,103,161,230,312,309,306,310,77,71,40,122,186,75,72,38,123,184,76,73,39,121,185,70,80,43,125,182,68,78,41,126,183,79,69,42,124,181,239,128,62,46,236,81,129,63,44,190,74,127,64,45,191,131,83,65,49,188,132,84,66,47,189,130,82,67,48,187,315,302,308,316 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*64, 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#31b39e995794136cb14e9cfb9c49dab141b331fe9ae7acf51f9a6bc9a2946638, M = {60} 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, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 21.

last edited by qawbecrdtey at 2026-10-01 22:26:58 · history