Equation 677 Database

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Magma 64b873885876…

magma 64b873885876
Size
321
Isomorphism class hash
64b873885876a90145b5662de23b6cf5dd1de7352c46c0d3d32c34b15e0a6987
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 22:54:49
Display reorder
300,17,123,126,192,205,18,121,127,193,203,19,122,128,194,204,20,119,125,195,208,21,120,124,196,206,22,231,232,197,207,15,115,132,198,211,16,113,133,199,209,14,114,134,200,210,118,11,131,201,213,116,12,129,202,212,117,13,130,236,237,311,315,303,302,248,262,261,263,260,246,253,252,254,255,247,257,256,258,259,251,272,273,274,275,249,264,265,266,267,250,268,269,270,271,243,284,285,286,287,244,277,276,278,279,245,281,280,282,283,297,242,296,298,299,289,240,288,290,291,293,241,292,294,295,320,318,319,317,57,28,188,171,228,224,26,186,169,77,56,27,187,170,78,53,24,191,174,75,54,25,189,172,76,55,23,190,173,74,48,34,183,177,71,49,32,184,175,69,47,33,185,176,70,30,51,182,179,73,31,52,180,178,72,29,50,181,235,227,313,304,308,307,37,91,0,60,143,35,92,2,58,144,36,93,1,59,145,40,94,4,63,142,38,95,5,61,140,39,96,3,62,141,43,97,7,66,135,41,98,8,64,136,42,99,6,65,137,100,46,10,226,138,229,44,225,67,233,101,45,9,68,139,305,309,301,316,87,218,146,159,103,85,219,147,157,104,86,217,148,158,102,90,214,149,162,106,88,215,150,160,107,89,216,151,161,105,82,222,152,165,109,83,223,153,163,110,84,221,154,164,108,220,81,155,168,230,239,79,234,166,112,238,80,156,167,111,312,310,314,306 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#c2d2ffbf4b11c3cb3cbc2e9e264bf213176e8d1ad1040891146c21601605ebcd, 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 22:54:50 · history