Equation 677 Database

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Magma 92cc3dceae4e…

magma 92cc3dceae4e
Size
321
Isomorphism class hash
92cc3dceae4ef576b7f4398b146977efcbf232a53470c4135cde24be9b5d38f7
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 22:54:53
Display reorder
300,1,48,178,35,189,176,0,33,190,49,177,50,2,34,191,51,174,3,31,192,52,175,4,32,193,53,173,5,30,194,237,236,46,41,195,184,182,47,39,196,185,183,45,40,197,180,186,42,37,198,181,187,43,38,199,36,179,188,44,200,302,304,316,313,273,241,272,275,274,265,264,266,267,242,269,240,268,270,271,244,257,256,259,258,245,261,260,262,263,243,253,252,254,255,297,296,247,299,298,288,289,248,290,291,292,293,246,295,294,281,280,250,282,283,284,285,251,286,287,278,277,276,249,279,319,318,317,320,142,22,57,166,229,58,140,164,227,23,59,21,141,165,228,18,56,138,162,225,19,54,139,163,226,20,55,137,161,224,148,63,28,172,235,146,64,29,170,233,147,65,27,171,234,62,144,24,168,231,60,145,25,169,232,167,61,143,26,230,307,311,306,301,71,150,217,209,130,215,69,210,128,151,216,149,70,211,129,153,213,67,208,126,154,214,68,206,127,152,212,66,207,125,239,223,156,238,136,75,221,157,201,134,76,222,155,202,135,219,73,159,203,132,220,74,160,204,133,205,218,72,158,131,315,305,314,309,86,10,122,107,94,123,87,108,92,11,124,9,88,109,93,6,121,85,110,90,7,119,83,111,91,8,120,84,112,89,77,113,16,105,100,78,114,17,106,98,79,115,15,104,99,116,80,12,101,96,117,81,13,102,97,103,118,82,14,95,312,303,310,308 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#c633edfa20dc6722982152bc303db7386181f99f3fbdfeb33272ccd5420b69f5, 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 22:54:54 · history