Equation 677 Database

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Magma b22bfae1aa7f…

magma b22bfae1aa7f
Size
321
Isomorphism class hash
b22bfae1aa7f995fe46dc6c4e98d94a2d1e6bc772079904abc22f6dfe11632ea
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 22:28:06
Display reorder
300,280,279,281,278,276,277,285,286,287,284,282,283,232,0,2,233,1,231,4,228,5,229,3,230,7,238,8,239,6,237,10,234,11,235,9,236,168,160,169,161,170,159,171,156,172,157,173,158,174,166,175,167,176,165,177,162,178,163,179,164,307,309,306,314,31,30,32,33,34,35,28,29,27,24,25,26,113,137,135,111,136,112,133,109,134,110,132,108,143,119,141,117,142,118,139,115,140,116,138,114,125,101,123,99,124,100,121,97,122,98,120,96,131,107,129,105,130,106,127,103,128,104,126,102,317,319,318,320,45,47,46,43,44,42,38,36,37,41,39,40,199,240,241,200,242,198,243,202,244,203,245,201,246,197,247,195,248,196,249,193,250,194,251,192,189,288,190,289,191,290,188,291,186,292,187,293,180,294,181,295,182,296,183,297,184,298,185,299,304,312,308,316,79,78,80,81,82,83,76,77,75,72,73,74,151,52,53,152,51,150,48,154,49,155,50,153,58,149,59,147,57,148,54,145,55,146,56,144,215,253,213,254,214,252,211,256,212,257,210,255,206,259,204,260,205,258,209,262,207,263,208,261,302,311,303,313,64,63,65,62,60,61,69,70,71,68,66,67,89,18,19,87,20,88,21,85,22,86,23,84,16,95,17,93,15,94,12,91,13,92,14,90,273,216,274,217,275,218,272,219,270,220,271,221,264,222,265,223,266,224,267,225,268,226,269,227,301,310,305,315 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 = {62} 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 22:28:07 · history