Equation 677 Database

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Magma 7913c54d5729…

magma 7913c54d5729
Size
321
Isomorphism class hash
7913c54d5729ae34a0e3dbf9a46d0bfd5a3295c8fe16faeab8578191afd3c64b
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 22:20:48
Display reorder
300,165,20,131,152,141,166,18,129,150,142,167,19,130,151,143,164,23,127,155,140,162,21,128,153,138,22,163,126,154,139,122,156,15,147,132,120,157,16,148,133,121,158,17,149,134,159,125,14,146,135,160,123,12,144,136,161,124,13,145,137,307,304,302,305,291,32,290,288,289,294,30,295,292,293,298,31,299,296,297,287,35,286,284,285,279,33,278,276,277,34,283,282,280,281,254,255,27,252,253,259,258,28,256,257,262,263,29,260,261,266,267,26,264,265,271,270,24,269,268,274,275,25,273,272,319,317,320,318,247,5,246,223,213,249,3,248,224,214,250,4,251,222,215,244,0,245,226,212,241,2,240,227,210,1,243,242,225,211,229,228,11,221,204,230,231,9,219,205,232,233,10,220,206,234,235,7,217,207,236,237,8,218,208,238,239,6,216,209,314,313,311,312,177,84,69,201,191,178,85,70,202,189,179,86,71,203,190,176,87,68,200,187,174,88,66,198,188,89,175,67,199,186,60,168,90,192,182,61,169,91,193,180,62,170,92,194,181,171,63,93,195,185,172,64,94,196,183,173,65,95,197,184,309,301,303,306,104,79,109,48,40,102,80,110,49,41,103,78,108,50,39,107,82,112,51,36,105,83,113,52,37,81,106,111,53,38,115,99,77,54,46,116,100,75,55,47,114,101,76,56,45,98,118,73,57,42,96,119,74,58,43,97,117,72,59,44,315,308,310,316 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#01253a2afae29ad04ad4e5938d81c583acd3aeb3895dbf3461a9c0b97e71e908, 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 22:20:49 · history