Equation 677 Database

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Magma c3e207b3aab3…

magma c3e207b3aab3
Size
321
Isomorphism class hash
c3e207b3aab30abe43771f24500945405aa28e207bd8a7b815a66f9dee68f824
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 22:28:02
Display reorder
300,214,213,215,212,210,211,204,205,206,207,208,209,64,220,221,65,219,63,216,60,217,61,218,62,226,70,227,71,225,69,222,66,223,67,224,68,278,197,276,195,277,196,281,193,279,194,280,192,284,203,282,201,283,202,287,199,285,200,286,198,303,302,312,316,113,112,111,108,109,110,118,119,117,114,115,116,162,132,133,163,134,164,135,165,136,166,137,167,138,160,139,161,140,159,141,156,142,157,143,158,121,144,122,145,120,146,124,147,125,148,123,149,127,150,128,151,126,152,130,153,131,154,129,155,317,318,319,320,88,87,89,86,84,85,93,94,95,92,90,91,232,72,73,233,74,231,75,228,76,229,77,230,78,238,79,239,80,237,81,234,82,235,83,236,288,171,289,172,290,173,291,170,292,168,293,169,294,177,295,178,296,179,297,176,298,174,299,175,304,308,311,315,249,251,250,247,248,246,242,240,241,245,243,244,36,262,263,37,261,38,258,39,259,40,260,41,253,42,254,43,252,44,256,45,257,46,255,47,96,57,97,58,98,59,99,56,100,54,101,55,102,48,103,49,104,50,105,51,106,52,107,53,307,301,310,313,32,31,30,34,35,33,29,27,28,25,26,24,7,21,22,8,23,6,20,10,18,11,19,9,12,5,13,3,14,4,15,0,16,2,17,1,181,266,182,264,180,265,184,269,185,267,183,268,187,272,188,270,186,271,190,275,191,273,189,274,305,306,309,314 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#3e7f78778326128ca89bcdb69266df7c07c66aee73c2a2e36b24ead92b52079d, 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 22:28:03 · history