Equation 677 Database

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Magma e7f5e29774c4…

magma e7f5e29774c4
Size
321
Isomorphism class hash
e7f5e29774c46075beeb9fbad99b3255cee94198643b0e4cb48c7493513f6416
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 23:00:16
Display reorder
300,98,20,182,41,93,96,18,180,39,94,97,19,40,181,95,101,23,185,44,92,99,21,183,42,90,100,22,184,43,91,15,104,188,47,84,16,102,186,45,85,17,103,187,46,86,107,14,191,50,87,105,12,189,48,88,106,13,190,49,89,305,311,307,302,261,250,263,262,260,252,251,254,253,255,256,249,257,258,259,272,246,274,273,275,265,247,266,264,267,269,248,270,268,271,241,285,286,284,287,242,276,278,277,279,240,281,282,280,283,296,244,298,297,299,289,245,290,288,291,292,243,294,293,295,319,318,320,317,59,146,71,65,24,57,144,69,63,25,58,145,64,70,26,62,149,74,214,213,60,147,72,205,204,61,148,73,210,209,152,54,77,224,225,150,55,75,216,217,151,56,76,220,221,53,155,80,237,236,51,153,78,229,228,52,154,79,233,232,303,301,315,314,134,38,194,110,121,132,36,192,108,122,133,37,109,193,120,137,34,197,113,124,135,35,195,111,125,136,33,196,112,123,29,140,200,116,127,27,138,198,114,128,28,139,199,115,126,143,32,203,119,130,141,30,201,117,131,142,31,202,118,129,308,312,304,306,164,3,83,170,67,162,4,81,168,68,163,5,169,82,66,167,2,215,173,212,165,1,206,171,207,166,0,211,172,208,9,159,227,176,226,10,160,219,174,218,11,161,223,175,222,158,8,239,179,238,156,6,231,177,230,157,7,235,178,234,309,313,316,310 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#edd749230bc58665165cb5ff86cf593765d0cefcd490b689f1cd7ce77c95b856, 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 23:00:17 · history