Equation 677 Database

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Magma a5e62361db0e…

magma a5e62361db0e
Size
321
Isomorphism class hash
a5e62361db0eff78e899b18bb51bda0cd2e4d32540c766ecb0385bad694193d8
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 22:27:01
Display reorder
300,53,232,28,220,205,51,233,29,221,206,52,231,27,219,204,49,24,228,216,208,229,25,50,217,209,48,230,218,207,26,226,34,238,59,211,227,35,239,57,212,225,33,237,58,210,30,222,234,55,214,56,31,223,235,215,32,224,236,54,213,308,312,310,307,99,269,271,268,270,100,272,275,273,274,101,265,266,264,267,98,255,252,253,254,256,259,96,257,258,97,260,261,262,263,293,294,292,105,295,297,298,296,106,299,288,290,289,107,291,279,276,277,104,278,102,283,281,280,282,287,285,284,103,286,317,320,319,318,42,244,139,4,148,43,245,140,5,149,44,243,138,3,147,45,142,240,1,144,241,143,46,0,145,47,242,2,146,141,10,137,250,40,154,11,135,251,41,155,9,136,249,39,153,133,6,246,36,150,37,134,7,247,151,132,8,248,38,152,303,316,315,302,202,130,160,76,108,203,131,161,77,109,201,129,159,75,110,198,156,126,72,111,127,157,199,73,112,200,128,74,113,158,82,166,121,193,114,83,167,122,194,115,81,165,120,192,116,162,78,124,196,117,197,163,79,125,118,164,80,123,195,119,301,314,309,305,63,181,171,87,12,64,182,172,88,13,65,180,173,89,14,62,170,184,86,15,185,168,60,84,16,61,183,85,17,169,93,177,187,69,18,94,178,188,70,19,95,179,186,71,20,176,92,190,68,21,66,174,90,191,22,175,91,189,67,23,306,313,311,304 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#3233330d12681148716a4d7ca0430e02a433d3f211b7945abf3bfa7e2eafe60e, 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 22:27:02 · history