Equation 677 Database

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Magma 9c3e43a6e9bc…

magma 9c3e43a6e9bc
Size
381
Isomorphism class hash
9c3e43a6e9bc6b17e1dfcabdc1e9d68321c4ed2a0398cd996775349fa604fead
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:17:03
Display reorder
380,171,166,176,150,155,160,216,221,225,230,235,211,113,108,109,110,111,112,323,318,319,320,321,322,122,123,124,125,120,121,246,251,256,261,265,241,103,104,105,106,107,102,276,281,286,291,295,271,114,115,116,117,118,119,200,205,181,186,191,195,126,129,146,148,127,128,352,341,353,355,370,361,375,343,334,366,174,169,179,154,158,163,218,223,229,234,239,214,101,96,97,98,99,100,301,300,302,303,304,305,80,81,82,83,78,79,248,253,258,263,268,243,91,92,93,94,95,90,278,283,288,293,299,274,72,73,74,75,76,77,204,209,184,188,193,199,84,89,85,86,87,88,349,331,335,358,373,364,378,350,351,369,170,165,175,151,156,161,215,220,226,231,236,210,145,140,141,142,143,144,329,324,325,326,327,328,2,3,4,5,1,0,245,250,255,260,266,240,135,136,137,138,139,134,275,280,285,290,296,270,10,11,6,7,8,9,201,206,180,185,190,196,147,133,149,130,131,132,337,330,354,356,371,360,376,345,344,365,173,168,178,153,159,164,219,224,228,233,238,213,47,42,43,44,45,46,316,317,312,313,314,315,56,57,58,59,54,55,249,254,259,264,269,244,67,68,69,70,71,66,279,284,289,294,298,273,48,49,50,51,52,53,203,208,183,189,194,198,60,65,61,62,63,64,348,336,339,359,374,363,379,342,332,368,172,167,177,152,157,162,217,222,227,232,237,212,34,35,30,31,32,33,311,306,307,308,309,310,17,12,13,14,15,16,247,252,257,262,267,242,28,29,24,25,26,27,277,282,287,292,297,272,39,40,41,36,37,38,202,207,182,187,192,197,20,19,21,22,23,18,338,346,333,357,372,362,377,340,347,367 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#09de7e296fafc11e1910887718202808c6591641f036fb4e85591d955a2aaea1, M = {72} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:17:04 · history