Equation 677 Database

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Magma 01da209a1bd4…

magma 01da209a1bd4
Size
321
Isomorphism class hash
01da209a1bd44b14384e2c93d3a6dbb22f522a5ce8c45d5eb763cd69700e1a97
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 22:33:02
Display reorder
300,178,23,126,107,32,176,108,21,127,30,177,106,22,125,31,180,19,128,217,209,179,20,129,110,238,247,207,220,109,29,183,28,124,105,37,181,26,122,103,35,182,27,123,104,36,25,184,120,101,33,208,233,121,102,34,24,248,244,216,210,315,308,302,305,98,280,282,283,281,99,287,284,286,285,100,279,277,278,276,97,293,294,295,292,95,296,298,299,297,96,289,290,291,288,89,272,274,275,273,90,265,266,267,264,91,269,270,271,268,256,92,258,259,257,260,93,262,263,261,252,94,254,255,253,318,317,319,320,6,145,75,163,224,205,246,245,76,134,7,162,144,74,223,206,147,78,165,136,8,148,79,166,137,9,146,77,164,135,10,143,73,161,133,11,141,71,159,131,12,142,72,160,132,139,13,69,229,222,140,14,70,158,130,138,236,241,228,221,311,303,310,313,63,0,54,115,189,64,116,2,55,190,65,114,1,53,188,66,4,57,118,192,67,5,58,119,193,68,3,56,117,191,62,16,52,219,187,213,17,212,112,235,61,18,51,113,186,15,59,50,218,249,204,240,211,243,234,237,60,49,111,185,306,301,316,307,47,153,171,199,84,48,197,154,172,85,46,198,152,170,83,43,156,174,195,87,44,157,175,196,88,45,155,173,194,86,39,151,169,203,82,40,150,168,201,81,38,227,232,202,215,149,42,230,251,214,226,239,231,250,242,225,41,167,200,80,312,314,304,309 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#5a6f57af4478d367dfac6487e89f811f842218c665866e576bd9224bcbc8a047, 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 22:33:03 · history