Equation 677 Database

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Magma 39313c7e5f25…

magma 39313c7e5f25
Size
321
Isomorphism class hash
39313c7e5f2567d28ab45047c58c8c885e39bc539412f164e983e80d1bc5c319
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 22:27:09
Display reorder
300,112,54,146,120,136,113,55,137,144,121,111,56,135,145,122,108,57,132,149,123,109,58,133,147,124,110,59,134,148,125,118,52,142,152,126,53,143,150,119,127,51,141,151,117,128,138,48,155,114,129,139,49,153,115,130,140,50,154,116,131,315,316,301,302,272,68,275,274,273,264,66,265,267,266,268,67,269,271,270,257,71,256,259,258,261,69,260,263,262,253,70,252,255,254,297,63,296,298,299,64,288,290,289,291,65,292,295,293,294,280,62,282,281,283,284,60,286,285,287,276,61,278,277,279,320,319,318,317,238,157,26,213,239,234,158,235,24,214,236,156,237,25,215,230,160,231,29,212,232,161,233,27,210,229,159,228,28,211,251,163,250,32,204,164,246,30,247,205,162,248,31,249,206,242,166,35,243,207,244,167,33,245,208,240,165,34,241,209,310,309,307,308,85,6,185,221,176,86,7,174,183,219,84,8,175,184,220,88,9,179,181,217,89,10,177,182,218,87,11,178,180,216,91,4,171,191,227,5,172,189,92,225,3,173,190,90,226,170,1,187,94,223,168,0,188,95,224,169,2,186,93,222,311,312,306,303,14,39,74,197,97,12,40,98,72,195,13,41,96,73,196,17,38,100,77,193,15,36,101,75,194,16,37,99,76,192,20,45,103,80,203,46,104,78,18,201,47,102,79,19,202,106,44,83,23,199,107,42,81,21,200,105,43,82,22,198,314,313,304,305 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#33fc7ab4b4817466950310b35dd4cd44cb4b00aed5b55945bbae0672c2180aa2, 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 22:27:10 · history